As shown in the figure, the height of an air column in a particular pipe is adju

Question

As shown in the figure, the height of an air column in a particular pipe is adjusted by changing the water level in the pipe. In a traditional experiment, a tuning fork is placed over the pipe, and the height of the air column is adjusted, by moving a reservoir of water up and down, until the pipe makes a loud sound, which is when the pipe's fundamental frequency matches the frequency of the tuning fork. If the speed of sound is 340 m/s, and an air column of 21.0 cm produces the loudest sound, what is the frequency of the tuning fork?

Explanation / Answer

The speed of the sound is

v = 2 L f

Here, length of the air column is L and frequency of the tuning fork is f.

Thus, the freqeuncy of the tuning fork is

f = v / 2L

Subsitute 340 m/s for v and 21.0 cm for L in the above equation,

f = v / 2L

   = 340 m/s / 2 (21 cm) (10-2 m/ 1 cm)

= 809.52 Hz

Rounding off three significant figures, the frequency of the tuning fork is 809 Hz

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