Equipment: 10 ft PVC pipe, rulers/measuring tape, cutters, corks, duct tape.

Though each team will have one report, two teams at a table can choose to work together as a larger group and each person do at least one of the needed pipes.

1. Each team will construct a flute that can, at least, play a full diatonic scale. Using the frequency lookup above. Use the first two columns of the Table 1 (headers provided after this textbox) to fill in the names and frequencies of a diatonic scale starting in the mid-range (say with G₃, or C₄). Any thoughts on why I suggested picking a note in the mid-range?
2. Record the type of scale you intend to use, and the key in which you will fashion your instrument.
3. For each note in column 1 of Table 1, use the frequency in column 2, and the equation v = lf with v = 340 m/s for the speed of sound to find the predicted wavelength of sound at this frequency. (This will correspond to the wavelength of the fundamental mode for a tube open at one end.) Record this in column 3.
4. Using the formula for wavelength of the fundamental mode for a tube open on one end provided on page 1 of this handout, compute and record the expected length of tube needed to produce this fundamental mode in column 4 of the table. Convert meters to cm when entering in the table (1 m = 100 cm).
5. In tubes of finite diameter, an end correction is needed to the length of the pipe. Remember that an open end of a pipe is a pressure node. But the air just outside the pipe is effectively adding inertia to the air in the pipe, making the frequency lower – this effect can be modeled by saying that the pipe appears to be effectively longer by an amount equal to 0.3*inner diameter of the pipe. In other words, in constructing your pipe, you must measure and subtract this length.
   Record the inner diameter of your pipe(in cm), and multiply this number by 0.3 (cm).
6. In the length w/ end correction column, column 5, subtract the number you found above from the predicted length value.
7. Finally, adjust the length of the column to account for the length of cork that will cap the other end. Insert the cork in a piece of pipe, mark and measure the length inside the pipe. Add this value to your pipe length, and  enter it in the final length column, column 6. This is the length you need.
8. Divide the labor (every person should do one pipe), measure the length of pipe and cut it.
9. Demonstrate your final instrument to the class by playing either individual flutes in concert or by combining them into one instrument using duct tape.

• This instrument consists simply of a membrane stretched over an empty container on which salt or sand is spread. When sound waves excite the air at the interior of the container, the salt or sand particles find the resonant patterns of the membrane, settling into nodes and moving on antinodes, much like the Chladni patterns we observed in the in-class demo.
• There are many ways to make a tonoscope. One suggestion is to take a large empty can (e.g. a coffee tin). Turn it upside down, sprinkle salt/sand on the surface, and place a phone or speaker inside on which you can blast loud music.
• Alternatively, find a large empty cardboard cylinder (e.g. oatmeal container). Cover the top with a balloon or plastic wrap stretched tight over the opening, held down with elastic bands or duct tape. You can then make a hole in the side large enough to fit a cardboard paper towel roll tube, and then sing into the tube to see patterns form on the membrane.
• See https://www.youtube.com/watch?v=P5WAlKx8QJE for further ideas.

• The name of this instrument translates literally to “water waves”. Originating in India (the first mention occurs around 400 BCE), it is constructed from a set of ceramic, glass or metal bowls or cups partially filled with water – the pitch is controlled both by the size of the bowl and the level of water in it. The Hornbostel-Sachs classification is a struck idiophone: 111.242.11 (Resting bells whose opening faces upward): it is played by striking with a wooden stick. This video gives you a sense of how it is played in Indian classical music: https://www.youtube.com/watch?v=TwzYjNR7uiA
• To build one, find a set of cups, glasses or bowls, and a wooden stick to strike them with – fill each with water till it reaches the pitch you want. See if you can play a piece of music on it. You can find one built by your TA Aniketh Acharya at this link: https://youtu.be/sEJGI7n8M6E

If you’re feeling ambitious and have tubes at your disposal (e.g. PVC, straws), follow the instructions above in the “In Person Lab” section and build a panpipe.