Question

Human audible frequency range is 20 Hz to 20 KHz. If velocity of sound in air is 340 m/s, the minimum wavelength of audible sound wave is
$\left( A \right)$ 0.17mm
$\left( B \right)$ 1.77mm
$\left( C \right)$ 17mm
$\left( D \right)$ 170mm

Answer 1

- Hint: In this question use the concept that speed of sound is the product of wavelength and frequency so use this property to reach the solution of the question.
Formula used – $v = \lambda f$

Complete step by step answer:
As we know speed of sound (v) is the product of wavelength ($\lambda $) and frequency (f).
$ \Rightarrow v = \lambda f$
So the wavelength is given as
$ \Rightarrow \lambda = \dfrac{v}{f}$.................. (1)
Now it is given that range of audible frequency is (20 Hz to 20 KHz)
And velocity (v) of sound = 340 m/s.
Now we have to find out the minimum wavelength.
So as we see that in the denominator of equation (1) there is frequency (f) so to minimize the wavelength we have to maximize the frequency.
So we have to use frequency (f) = 20 KHz = 20000 Hz.
Now substitute the values in equation (1) we have,
$ \Rightarrow \lambda = \dfrac{{340}}{{20000}} = 0.017$m
Now as we know that 1mm = 0.001 m
Therefore 0.017m = 17 mm
Therefore, $\lambda = 17$mm
So this is the required answer.
Hence option (C) is the correct answer.

Note – Whenever we face such types of questions always recall the direct relation between velocity of sound, wavelength of audible sound and audible frequency, then we want the minimum wavelength so we have to use maximum frequency so simply substitute these values in the equation and simplify, we will get the required answer.