Question

A source is producing 1500 waves in 3 seconds. If the distance covered by a compression and an adjacent rarefaction be 68 cm, find: (a) frequency, (b) wavelength, and (c) velocity, of the sound wave.

Answer 1

Frequency: 1 Mark
Wavelength: 2 Marks
Velocity: 2 Marks

(a) Frequency. We know that frequency of a wave is the number of waves produced in 1 second
Here, No. of waves produced in 3 seconds = 1500
So, No. of waves produced in 1 second $=\frac{1500}{3}$
= 500
So, the frequency of this sound wave is 500 hertz.

(b) Wavelength. In a sound wave, the distance covered by a compression and an adjacent rarefaction is equal to its wavelength. This distance has been given to be 68 cm. So, the wavelength $\left(\lambda \right)$ of this sound wave is 68 cm.

(c) Velocity. The formula for calculating the velocity of a sound wave is:
$v=f\times \lambda$
Here, Frequency, f = 500 Hz (Calculated above)
And, Wavelength, $\lambda =68cm$ (Calculated above)
$=\frac{68}{100}m$
= 0.68 m
Putting, these values of f and $\lambda$ in the above formula, we get:
$v=500\times 0.68$
= 340 m/s
Thus, the velocity (or speed) of the sound waves is 340 m/s.