Today is 11 January 2011 -- Sound wavelengths and frequencies

Its fun to see how science can be demonstrated with ordinary things. Today we explored sound frequencies using test tubes (or bottles), a meter stick, a candle and a home-made air cannon. This is what we did:

1. Air cannon -- For 99 cents I bought a 2-quart water bottle. I cut off the bottom and got a large balloon. I tied off the mouth of the balloon, then cut off the part of the closed end. I s--t--r--e--t--c--h--e--d the balloon over the bottom of the bottle. I should mention that in cutting off the bottle bottom, I left the rounded part so the balloon would not be punctured by sharp, plastic edges. To keep the balloon from slipping off the bottle, I wrapped the joint between balloon and bottle with electrical tape. Then, when I pulled on the knot where the mouth of the balloon had been, and released it, a "ball" of air shot out of the bottle mouth.

2. Flute -- We used test tubes. The ones on hand were 9.5 cm long, about 1.5 cm in diameter. By blowing over the open mouth of the test tube, we caused a pressure difference which made the tube vibrate. This vibration caused sound of a specific wave length. When we put water in the test tube, we changed its length. As the effective length of the tube shortened, what happened to the pitch of the sound? Did the loudness of the sound depend on the pitch or how hard the students blew across the tube? What happened if the tube was blown into instead of across the mouth? For more information, go to the link "Standing waves and Wind Instruments". There is more information than discussed in our text book (Activity 3, "Sounds from Vibrating Air."

3. Frequency -- We can find the frequency of the sound from the vibrating column of air for any length of tube. The equation is f = v / λ where f is the frequency in cycles per second, v is the velocity of the air and λ is the wavelength. We know that in a tube closed at one end, the wavelength of a vibrating column of air is four times the length of the tube. Another way of saying this is that 1/4 the wavelength fits in the column. If we can determine the velocity of sound in air, we can find the frequency of the sound.

There are two ways we can look at the velocity. One way is "fun," but maybe not so accurate. The other way is by scientific measurement. Lets say you are in a race. On your mark, set, GO! The starter fires his pistol. First you see the puff of smoke from the pistol, then you hear the sound of gunfire. You see the puff of smoke first because light travels so much faster than sound. In normal, still air, sound travels 1100 feet per second. You can substitute the values for the wavelength and the velocity in the equation, above. When you do so, you get: f = (1100 ft /sec x 30.48 cm / ft) / (9.5 cm X 4) = 882 per second.

O.K. Now, lets lay a meter stick on the table. We put a candle at "0 cm" and the air cannon at 100 cm. Students timed how long it took the pulse of air to travel 100 cm and cause the candle flame to flicker or be extinguished. Use the equation above to find out the frequency this way. Which answer makes more "sense" to you? Why?