Wednesday, October 22, 2014

A blade of grass makes sound- Sound Sandwich

If you pick a blade of grass or a leaf, stretched it in between your fingers or thumbs, and blow into the gap you will hear a high pitch sound. A lot of our students have had played with this effect. The working of a sound sandwich instrument, which can be made using simple items like craft sticks, a straw, one wide rubber band, two smaller and a narrow rubber band is no different in working as a blade of grass sandwiched between fingers and thumbs.
How to make a sound sandwich?
Stretch a wide rubber band length-wise over one of the craft sticks, and cut two pieces of straw, each about an inch to 1 ½ inches (2.5 to 3.8 cm) in length.
Put one of the small straw pieces under the wide rubber band, about a third of the way up from one end of the stick.
Take the second craft stick and place it on top of the first one, wrap one of the smaller rubber bands around the end of the stick a few times, about ½ inch (1.25 cm) from the end, on the same side where you placed the straw.
Make sure the rubber band pinches the two sticks tightly together. Take the second small piece of straw and place it between the two craft sticks, at the opposite end. This time, though, place the straw on top of the thick rubber band, so it sits just under the top craft stick. Wrap the second small rubber band around the loose end of the stick, about ½ inch (1.25 cm) from the end. When you are done, both ends should be pinched together and there should be a small space between the two craft sticks.
When your sound sandwich is complete, put your mouth in the middle, as if playing a harmonica, and blow. Notice that you can make different sounds by blowing through different areas of the instrument, blowing harder or softer, or by moving the straw closer together or farther apart.
What’s going on?
When you blow into the Sound Sandwich, you make the large rubber band vibrate, and that vibration produces sound. Long, massive objects vibrate slowly and produce low pitched sounds; shorter, less massive objects vibrate quickly and produce high-pitched sounds. The tension of a rubber band also will change its pitch: higher tension leads to higher-pitched resonance.
Reference: Exploratorium Teacher Institute (2009). The Exploratotrium Science Snackbook: cook up over 100 hands on science exhibits from everyday materials (revised edition). Robert J. Semper: United States of America. 

Tuesday, October 14, 2014

PET Bottle Membranophone

The PET (Polyethylene terephthalate, the plastic found in most platic bottles) bottle Membranophone is fun to make and even more fun to play. Using simple materials like a clean empty plastic bottle, a balloon, a rubber band, a straw, and A4 size paper we can make and play with one. This instrument produces sound from a vibrating stretched membrane or balloon.
 How to make:
Get a PET bottle and measure down about 3 inches (7.5 cm) from the top of the bottle. Using scissors, cut along the measured line. Make sure you cut evenly along the edge. Trim off any bumpy spots and recycle the bottom of the bottle. You will need the top half of the bottle to work with. Take out a punching machine and punch a hole near the cut edge of the top half bottle as far as you can get it. Put the straw through the hole to test it for size. It should be a tight fit. If the hole isn’t large enough for the diameter of the straw, re-punch in nearly the same spot to widen the hole a bit. Cut the neck off the balloon to form a sheet of elastic material- a membrane. Stretch the membrane over the hand cut opening of the bottle, making sure that the hole you punched in the side does not get hidden by excess material. Attach the membrane to the bottle with a rubber band. Wrap the rubber band around the bottle several times, making sure that the membrane is taut. Twist the cap off the bottle and set it aside. Roll a piece of A4 size paper into a tube, making it as tight and straight as possible. Put the rolled up tube into the neck of the bottle, where the cap had been. Let go of the tube when it barely touches the bottom of the membrane. It should fit securely in the hole. Tape it to the neck of the bottle so it stays in place. Insert the straw into the punched hole on the side of the bottle, and you’re ready to play.
Now that your instrument is ready, simply blow into the straw on the side of the bottle and your pet bottle Membranophone should play.

What’s going on?
As you blow into the straw, you create pressure in the space between the outer wall of the paper tube and the inner wall of the water bottle. That pressure forces the membrane to rise, allowing air to flow into the top of the tube and escape out the bottom.
As the air escapes, the membrane returns to its position. But as you continue blowing air into the instrument, you force the membrane to rapidly rise and fall, over and over again. If you place your finger over the top of the membrane, you can feel it vibrate. These vibrations produce sound.  

Exploratorium Teacher Institute (2009). The Exploratotrium Science Snackbook: cook up over 100 hands on science exhibits from everyday materials (revised edition). Robert J. Semper: United States of America. 

Tuesday, October 7, 2014

The sound and straw

By cutting the two lips of a soda straw, flattening the end, and blowing with just the right pressure, we can make sounds vibrate in the straw.
Flatten one end of the straw by sticking the end in the mouth, biting down with teeth, and pulling it out. Do this for several times to make flexible, flat-ended straw. Cut equal pieces from each side of the flat-ended so that straw has two lips at the end. Put the straw in your mouth and blow into the straw. You will probably have to experiment with blowing harder and softer while biting down with different amounts of pressure until you make the straw sing.
The monks here at CGI make straw reeds in same way to use it with Gyaling. Gyaling literally means "Indian trumpet" and is used during the monastery puja (chanting and prayer) and is associated with peaceful deities. All the monks know how to make and use this simple straw reed. Normally when they make them the reeds are shorter in length and can produce high pitch sounds. The reed goes on top of the Gyaling to make it sing.
So, the question we asked our class was ‘’What makes the straw reed produce sound?’’ To this question, the 20 students have responded with a few one-word guesses- air, pressure, vibration, high, low, hole etc. They were some pretty exciting responses. In fact, all the words that can explain the working of the straw reeds were spoken by them.
With supporting responses from the students, it was quite convenient for me to discuss the working of the reeds- when we blow through the straw, there is high pressure in your mouth. As air rushes through the straw, the pressure in the straw drops, and the high pressure outside the straw pushes the sides of the reed inward, closing off the flow. The pressure then builds inside the straw and pops the reed open again. This causes the vibration of the straw lips. When the reed vibrates at just the right frequency, there we hear loud, buzzing notes.

This is not only a good lesson on acoustic physics but also a fun way to reuse a straw.

Monday, September 29, 2014


With the end of the blessed rainy day and the beginning of the early days of the eight month of the lunar calendar, a few students have sown some more seeds in their gardens- such as bean, coriander, radish, spinach and lettuce.
The continuous rain water from the last few days has nurtured the soil making it favorable for seed’s growth, in this young season- FALL!
This time of  year is good for sowing spinach, bean, coriander, radish etc. For some vegetables we weren’t quit sure of the perfect time to plant - like egg plant, pumpkin etc- but we have decided to experiment with their growth in our garden by planting them now.
Working in the garden is a great opportunity for the students to learn with their hands. Right from the start of the garden work- digging an earth, holding a spade and pick axe and manually using one’s energy to unfurl the soil- there are many lessons being learned and many calculations being done mentally, but unconsciously.
The student’s decision to use a pick axe instead of  spade to open the soil has its own science behind it. The students are their own architects in the garden, shaping their own beds, calculating, measuring, and designing them in whatever way they desire. The depth, width and the line that they keep track of while sowing seeds are an estimation and math concept in themselves.
While there are so many things students can learn from the garden classes, the focus  in the last session was on finding an area and perimeter of their own beds. The students have used measuring tape to find the length and breadth of the beds. After they have collected their respective bed’s basic data they were ready to calculate and found the actual area of their beds. It was quite interesting to see the students measure and take their own responsibilities in their learning by doing from the context. I have also seen them cooperate with friends in finding the measurements.
From the previous planting we have now green sprouts of bean and squash that have grown from six to eight centimeters tall from the ground. The spinach and coriander have sprouted a centimeter above the bed, exposing their two leaves of early growth, ready for photosynthesis.

We all are waiting to see the gradual growth of our vegetables.

Wednesday, September 24, 2014

Sowing the seed

A squash sprout
It’s late in the seventh month of the lunar calendar, and Tshering Phuntsho, Pema Dorji and Leki Dorji have sown bean, spinach, and squash seeds in their gardens to experiment with the growth of different vegetables. 
The sowing of the seeds was accompanied by question marks in their head about the right time for planting in Dewathang. A few students have said that the sowing season in Dewathang is after the celebration of the Blessed Rainy Day or sometime in the eighth month of  the lunar calendar. However, we have decided to sow the seeds and check their growth. After three days of sowing seeds, we have checked the garden and to our excitement we found fresh squash, bean and spinach sprouts emerging out from the soil.
There are hopes from our students that these vegetables will grow, nevertheless rainy season in Dewathang is not yet completely stopped. Some students are concerned about the last heavy rain for the summer yet to fall, which would hamper the new vegetable sprouts in their gardens.
Samdrup Tshering and Leki Dorji transplanting cabbage sprouts.
On the other hand Leki Dorji and Samdrup Tshering have transplanted their cabbage sprouts in their beds. They have brought two bunches of the sprouts from the neighbor’s to plant in their gardens. Both of them were quite positive with their transplantings and were looking forward to productive growth. 
A bean sprout
Karma Phunstho has sown the lettuce seeds in his small bed and he was confident that his lettuce growth will be successful. A few students are willing to wait for the last heavy rain to go away before they sow their seeds and they are working to extend and add more new beds.

Karma Phuntsho's Lettuce garden 

Saturday, September 13, 2014

The calculator on the finger tips- Math trick

There is very convenient Math Trick to easily multiply the numbers from 6 to 10 using ones own fingers. We call this, calculator on the finger tip. It is used to teach children to learn tricks about multiplication time tables without any external resources. It also provides our students an opportunity to perfect it, anywhere and anytime just playing with their fingers after learning the trick.  
After teaching this trick in the class, most of the students who have struggled to memorize the times tables before, have admitted it to be very easy for them to calculate. It was amazing to see how handy the fingers are to calculate, besides providing mental calculation opportunity for an individual.
I remember how my students struggled to memorize the times table, especially starting from 6 to 9.  For some, they even took so long to memorize up to 5. Besides, it was of less practical memorizing, when there are gaps of few weeks and few months. The students keep on forgetting and they have to rememorize again (however not so difficult this time).    
So, in the following paragraph I am going to show you the trick. Well, first put your both hands in front of you and ascribe values from 6 to 10 to each finger starting from little finger to thumb. So, the values of  little fingers are 6, 7 for ring fingers, 8 for middle fingers, 9 for forefingers and 10 for thumbs.
How to multiply?
Step 1: Choose the numbers to multiply. For Example: 7x8   
Ste      2: Put together the fingers, whose values you want to multiply. Here, it is ring finger of the left hand and middle finger of the right hand.
Step 3: Now, count the touching fingers and the ones below them. Each of this finger will have the value of 10. So, if there are 5 fingers then the values are five times ten (5*10), which is equal to 50. Mentally retain this number in your head. 
Step 4: Now, multiply the fingers above the ones touching fingers. So, multiply 3 on left hand side with 2 on right hand side. We will get (3*2) 6.
Now mentally add 50 and 6 (50+6), the answer will be 56.
We can use this trick to calculate the times table of 6, 7, 8, 9 and 10, what amongst are the most difficult to calculate and memorize for almost all the students.

Tuesday, September 9, 2014


On last two Saturdays, our twenty students were drenched in sweat to make a vegetable garden and compost pit beside the residence of Drubgyud Tenzin Rinpoche. Rinpoche was very kind to offer his garden to the class as a learning space for the students. The continued monsoon rain in Dewathang has loosened the soil and it was quite easy for us to dig the earth. So far we have dug 20 small beds and we are getting set to sow seeds in a few weeks of time.
It’s been quite some time, waiting for a bright and dry day to begin work in the new vegetable garden. We will be experimenting in the garden with growing different seeds that are locally grown in Dewathang and also few other seeds from other place.
It was quite surprising for us to come up with long list of vegetables that can be grown in Dewathang: potato, eggplant, coriander, spinach, bean, pumpkin, squash, spring onion, cabbage, cauliflower, ginger, cucumber, tomato, radish, carrot, turnip, lettuce, etc. The list goes on. There are abundant vegetables we can grow in our garden.  
We also discussed about the right time to sow seeds in Dewathang. Students have pointed out that the summer season is usually not a good time for sowing seeds because of heavy rain fall. A few of them said we can sow seeds after blessed rainy day (which falls sometime in late September). Tshering Samdrup, a student from our class has called his parents, to ask about sowing seasons and few others have enquired to villagers. I'm happy to see how they take their responsibilities in learning.
It was quite a challenging for all of us, especially to make a bed on steep slope and leveling it, however with joined effort and cooperation we could managed to make the beds. The students have used unwanted logs and planks to make a supporting wall for the beds and to make it hold in a position they have used strong pegs.

Now, jointly we have agreed to sow seeds after the blessed rainy day. The beds are yet to finalize this weekend.

Tuesday, August 26, 2014

Stomp Rocket

The students brainstormed and played with the parts of the stomp rocket that I made for one of my science projects at The Exploratorium Teacher Institute training program in San Francisco. They had to figure out how to assemble it into the rocket stomp. I asked them an open ended question in the beginning to welcome their creative ideas and new designs from the rocket parts. So, I asked “what can you make out of these parts?’’ It was quite interesting to see the students collaborate their ideas and experiment assembling different models. They came up with different shapes of the alphabet (T, F, h), number (4) and other shapes with their own explanations.
After they tried every possible shapes and designs that they could think of, I asked them to come up with a model of a rocket stomp or a launcher. The students started to rush their ideas into remodeling a rocket stomp. After they figured out their rocket launcher, I gave them some guidance to make the launcher stable.
The next assignment was an art project to make a rocket out of paper or transparent little hard plastic cover or chart paper, cello tape and scissors. I demonstrated how to make a rocket using paper, and asked them to come up with their own designs and shapes for their respective rockets.
The students came up with their creative rockets: some are shorter, others are longer with tails attached and some are without a tail. Everyone was happy with their own rocket and assumed that their rocket would travel to the highest point in the sky. I have also seen students teasing each other with their rockets.
Finally, it was time for all of us to launch our rockets. We all went outside, in front of the guesthouse yard at Chokyi Gyatsho Institute and gathered around a rocket stomp. I told my dear boys that we are going to ‘’estimate’’ the distance travelled by each rocket. The word ‘’estimate’’ was introduced in the class with some daily practical examples (we estimate salt to add in the curries, etc.), before we came outside and they have quite a good understanding of this vocabulary. The students presented the launching of their rockets according to the alphabetical order of their names. Other students in the audience surrounded the rocket stomp, counted down from 3 to 0, while a stomper was ready to give a big stomp on the two liter plastic bottle to push the rocket into the sky.
In the process of launching, the students discovered how a rocket works in general and which of their rockets would travel the longest distance. They knew that a rocket with an attached tail travels further. They also said that a rocket with pointed head, slim, long, straight and airproof ones travel further.
After launching each rocket, I have asked them to estimate the distance travelled by that rocket. They came up with different estimations: 20 feet, 30 feet, 40 feet, 50 feet, etc.
Mr. Sangay Nidup’s rocket travelled the highest distance with an estimated height of more than 50 feet, followed by Mr. Dema Gyempo.

Sunday, August 3, 2014

Feel the temperature

When I was at the Exploratorium in San Francisco, I learned a technique for grouping students for activities in a class by shaking hands and feeling the temperatures. The temperature of human hands varies from individual to individual. Human hands can easily sense the temperatures of other hands.
To investigate we can ask our students to shake hands with other students in the class and notice the temperature of the other hands. Most likely, the students will have hotter or colder than their own hands. 
After shaking hands with many people, arrange them in a line from hottest hands at one end to coldest hands at the other. Then have the hottest handed person and the coldest handed person divide the line into two equal groups- Hot handed group and cold handed group. We can also extend this activity by making the hot handed person and the cold handed person go down the line shaking hands with everyone else to find out the differences.
What’s going on?
Human hands have different temperatures. The temperature depends on the metabolic rate and circulatory system of each individual. If a person’s vascular system is dilated (which is what we call vasodilatation), their hands tend to be hotter, if it is constricted (vasoconstriction), their hands tend to be colder.
We can also try this activity with an adult who smokes and drinks alcohol. First do the above activity then allow the smoker to take a break to smoke . When they return have them shake hand and experience the difference. Nicotine in cigarette smoke is a vasoconstrictor and will cause their hands to become cooler. On the other hand alcohol is a vasodilator and will cause their hand to become warmer. 
In addition to using this information for grouping a class, it can be the entry point to a number of lessons, from anatomy to physics even hygiene. Be sure to wash your hands after touching so many people, hands are the number one way to spread germs.

Tuesday, July 29, 2014

The Pinhole Investigation

The Pinhole Investigation is a very simple activity, but very affective to make students understand and confirm for themselves that the image that comes through a pinhole is reversed from top to bottom and left to right. This activity will provide our students with an opportunity to think and discuss why images appear in reverse, from top to bottom and left to right.
To make a pin hole, we need a sheet of black construction paper, 1 cardboard toilet tissue tube, 1 piece of aluminum foil, 1 piece of wax paper, and 4 rubber bands.
How to make
I will share how I made my pinhole at The Exploratorium Summer Institute Teacher Training Program. I placed the aluminum foil over one end of the toilet tissue tube and secured it with a rubber band. Then I placed the wax paper over the other end of the toilet tissue tube and secured it with a rubber band. Here we were instructed to be careful with the wax paper to keep it as smooth as possible because it is a screen.
Next, I rolled the black construction paper lengthwise around the tube, keeping the aluminum foil end exposed. The wax paper end of the tube became the middle of the black construction paper tube. Later, I came to know that the black tube has its purpose to allow us to see the images more clearly.
Finally, I used a pin to make a hole in the aluminum foil. We were told that sometimes the hole must be enlarged to see the image more distinctly, but it was better to start with a small hole and then make it larger if needed.
What next?
After making a pin hole, each student can take the viewer outside and look at houses, trees, cars, etc. through the open end of the tube. Ask this question to students: What do you notice?
We tried the viewer inside the classroom looking at one red and one green light bulb. We can also try it with a candle.
The following were a few questions we discussed in the class, and we can ask similar questions with the students: Why is the image reversed? How can I make it turn right-side up? How can I make the image clearer? How can I make the image larger? What if I used a larger tube, a longer tube, a larger hole, etc.?

Saturday, July 26, 2014

The Fan Cart

The classic physics problem, the action-reaction pairs in Newton’s Third Law can be explored from one of the projects I have made at The Exploratorium Summer Institute Teacher Training Program.
Let us ask a question to ourselves: “If a sailboat is stuck because there is no wind, is it possible to set up a fan on deck and blow wind into the sail to make the boat move?” The answer to this question can be solved by constructing a “Fan Cart” using simple materials, e.g. a cart, a motor, 4 CDs, a few drinking straws, a fan, a sail, straight round sticks, Velcro fasteners, a pair of small batteries and a battery case.
Make the fan cart look like the one in the pictures or you can design your own. 

Now notice the following observations:
1. Attach the sail and then attach the fan to the cart with Velcro so that it will blow air towards the sail when it is running. Turn on the fan, and observe what happens.
2. Leave the sail in place, but remove the fan assembly and turn it around (or leave the fan assembly in place and reverse the electrical connections to the motor), so that the fan will blow air away from the sail when it is running. Turn on the fan, and observe what happens.
3. Remove the fan assembly, and hold it in your hand while it blows air towards the sail. Observe what happens.
4. Replace the fan assembly so that it will blow air towards the sail when it is running, but then remove the whole sail assembly. Turn on the fan, and observe what happens.
5. Return to the original assembly, with the fan and sail both attached to the cart, and the fan blowing air towards the sail. Now insert a stiff piece of paper between the fan and the sail, and observe what happens.

What's going on?
Here is a summary of the first result from the situations above:
1. Cart doesn't move.
The behavior of the cart is a classic example of Newton's Third Law: For every action, there is an equal and opposite reaction.
In case 1, the fan pushes the air forward, and the air pushes the fan backward. A crucial thing to keep in mind is that the action and reaction forces - often called an action-reaction pair - do not act on the same object. If this was all that was happening, the cart would move backwards; the fan would be pushed backward, and since it's attached to the cart, the cart would be pushed backwards also.

Try to identify the action-reaction pairs in cases 2, 3, 4 and 5 and use them to predict why the cart behaves as it does.

Thursday, July 24, 2014

We can’t believe all that we see

Without a boundary, it's hard to distinguish different shades of gray. Sometimes we can't believe all that we see. Two slightly different shades of the same color may look different if there is a sharp boundary between them. But if the boundary is obscured, the two shades may be indistinguishable.
To try this experiment we can use the image provided below. Attach the white thread tail above the boundary between the two pieces, so that it hangs down and covers the boundary.
The tail like thread is used to obscure the boundary between two gray areas. We see one uniform gray area when the tail is in place, and two different gray areas when the tail is removed. But I have never seen the truth before the experiment. The truth in both gray areas is they are really identical in grades from light gray at one edge to dark gray at the other. In general, our brain ignores slight gradations in gray shades.
If we try this activity with our friends, most of them will see a uniformly gray piece of paper with a rope hanging down the middle.
What is going on?
Actually, the two rectangles are exactly the same. At the right edge both rectangles are light gray. Both become darker toward the left. Where the rectangles meet, the dark part of one rectangle contrasts sharply with the light part of the other, so you see a distinct edge. When the edge is covered, however, the two regions look the same uniform shade of gray.
It is difficult to distinguish between different shades of gray or shades of the same color if there is no sharp edge between them. If there is an edge between the two shades, the difference is obvious.
Your eye-brain system, however, condenses the information it obtains from more than a hundred million light-detecting rods and cones in the retina in order to send the information over a million neurons to your brain. Your eye-brain system enhances the ratio of reflected light at edges. If one region of the retina is stimulated by light, lateral connections turn down the sensitivity of adjacent regions. This is called lateral inhibition. Conversely, if one region is in the dark, the sensitivity of adjacent regions is increased. This means that a dark region next to a light region looks even darker, and vice versa. As a result, your visual system is most sensitive to changes in brightness and color.
When the thread tail is absent and the normal boundary is visible, lateral inhibition enhances the contrast between the two shades of gray. The bright side appears brighter and the dark side darker. When the tail is in place, the boundary between the two different grays is spread apart across the retina so that it no longer falls on adjacent regions. Lateral inhibition then does not help us distinguish between the different shades, and the eye-brain system judges them to be the same.

Wednesday, July 23, 2014

A Simple Oscilloscope

By humming, singing, or talking one can create a variety of cool laser light patterns. This device will allow one to see sound as vibrations or pressure waves. It is called ‘’Vocal Visualizer or Simple Sound Oscilloscope’’ and is one of my first projects at the Exploratorium Summer Institute Teacher Training Program.
I will share how to make this simple device and what is the science behind the working of the device.
We have to cut the pipes into different sizes and arrange it as shown in the picture. Arrange the elbow and “T’’ joints and insert according to the image. Attach the vibration chamber which is made out of drain pipe, balloon and small mirror. Insert the laser into the central single pipe as shown.  Carefully point the laser at the mirror attached to the membrane.
Aim the device on the wall, screen, floor or other reflective surface. Hold the device close to the mouth and hum, sing or just make some weird noises.   
As we make noise, changing the pitch (frequency) and volume (amplitude) we will see a different kind of patterns created on the wall.
What is going on?
When we make sounds, we cause air molecules to vibrate. These vibrating molecules strike one another and hit the rubber membrane. The membrane vibrates, which causes the mirror to wiggle. The laser light bounces off this wiggling mirror, tracing out various shapes and patterns that we can see.
Different amplitude and frequency of sounds coming from your mouth in turn causes different shapes and patterns.
Some shapes look chaotic, others more regular and repeating. Various frequencies will cause the rubber membrane to dance around in resonant vibration modes, in effect creating fluctuating waves. This will be fun for students to learn and play.

Tuesday, July 22, 2014

Colored Shadows: Not all shadows are black

A prism breaks white sunlight up, spreading its component colors out into a spectrum of light visible to the human eye stretching from red through yellow, green and blue to violet. Scientists analyzing these colors find that they have a wave nature, and that one given wavelength of light is perceived as one color when viewed by a person. However, there are colors which do not occur in the spectrum, such as magenta. These colors can only be created when two different wavelengths hit the same spot on the retina at the same time. Without human perception there is no color magenta. Indeed, there is no white either. To understand the colors we must understand the human retina.
The retina of the human eye has three receptors for colored light: one type of receptor is most sensitive to red light, one to green light, and one to blue light. With these three color receptors we are able to perceive more than a million different shades of color.
When a red light, a blue light, and a green light are all shining on the screen, the screen looks white because these three colored lights stimulate all three color receptors on your retinas approximately equally, giving us the sensation of white.
With these three lights you can make shadows of seven different colors: blue, red, green, black, cyan (blue-green), magenta (a mixture of blue and red), and yellow (a mixture of red and green).

When red, R, green, G, and blue, B light shine onto the retina in roughly equal amounts, then humans perceive white, W. So we can say that W = R+G+B.

When red and green light shine on the screen, humans perceive yellow. So Y = R+G. Now yellow is also a color of the spectrum, which means that yellow is the color humans perceive when the retina is illuminated by a single wavelength of light. The single wavelength for yellow is between the wavelengths for red and green, and the yellow causes both the red and green cones to fire nerve impulses. The electrical signal sent to the brain when the eye is illuminated by one wavelength of yellow is similar to the signal sent to the brain by the combination of two wavelengths R+G.

Cyan, C, is a color of the spectrum. The wavelength of cyan light is midway between the wavelengths of blue and green. The crayon that used to be called blue-green is now called cyan, C. Cyan can also be created by adding blue light to green light. C = B+G.
When we mix blue and red light, our eye perceives the color magenta, M. Magenta is not a color of the spectrum: no single wavelength of light can produce the color sensation called magenta. M = R+B.