The speed of sound in air is 340 m/s. The shortest air column, closed at one end, which will respond to a 512 Hz tuning fork is approximately:
A) 4.2 cm
B) 9.4 cm
C) 17 cm
D) 33 cm
E) 66 cm

Question

Quizplus · Accepted Answer

The resonant frequency of a closed pipe is given by:
f = (2n-1)v/4L
where n is an integer, v is the speed of sound, and L is the length of the pipe.
For the first harmonic (n=1), f = v/4L
We are given f = 512 Hz and v = 340 m/s.
Therefore, L = v/4f = 340/(4x512) = 0.166 m = 16.6 cm.
However, this is the length of an open pipe. For a closed pipe, the length will be half of the wavelength, which means we need to add one extra half-wavelength to the length. The wavelength of a 512 Hz wave is:
lambda = v/f = 340/512 = 0.664 m = 66.4 cm.
So the length of the closed pipe will be (16.6 + 33.2) cm = 49.8 cm. Since the pipe is closed at one end, we need to divide this by 4, giving a final answer of 12.45 cm, which is closest to choice C (17 cm).

The Speed of Sound in Air Is 340 M/s