How do you Solve this Sound Word Problem?

Question

A hollow tube of length L, open at both ends as shown above, is held in midair. A tuning fork with a frequency fo vibrates at one end of the tube and causes the air in the tube to vibrate at its fundamental frequency. Express your answer in terms of L and fo.

(a.) Determine the wavelength of the sound.

(b.) Determine the speed of sound in the air inside the tube.

(c.) Determine the next higher frequency at which this air column would resonate.


The tube is submerged in a large, graduated cylinder filled with water. The tube is slowly raised out of the water and the same tuning fork, vibrating with frequency fo, is held a fixed distance from the top of the tube.

(d.) Determine the height, h, of the tube above the water when the air column resonates for the first time. Express your answer in terms of L.

Answer 1

a) A tube that is open at both ends has displacement antinodes at both ends. This corresponds to a wavelength equal to 2L.

b) f = nc/2L for the fundamental, n=1, which means c (the speed of sound inside the tube) = fo * 2L

c) f(2) = 2(fo *2L)/2L = 2fo

d) This situation is a tube that is open at one end and closed at the other. The formula for this situation is: f = nc/4L (n=1,3,5...)

So f=c/4L (2fo)/4L = fo/2L (subbing in the expression for c in terms of fo.)

Answer 2

a