Question

If the speed of sound in air is 340 m/s, what is approximately the length of the shortest air column closed at one end that will respond to a tuning fork of frequency 198 Hz?

Answer 1

Answer:

42.9 cm

Explanation:

given,

speed of sound, v = 340 m/s

Frequency of tuning fork, f = 198 Hz

The length of the shortest air column closed at one end.

this is the case of the standing wave.

L = N λ

N = the number of complete sine waves in the standing wave.

The standing wave in the problem is the first harmonic of a pipe open at one end.

N = 1/4

we know,

v = f λ

340 = 198 x λ

λ = 1.717 m

now,

L = N λ

$L = \dfrac{1}{4}\times 1.717$

$L = 0.429\ m$

   L = 42.9 cm

minimum length of the required pipe is 42.9 cm.