Question

A body is vibrating 7200 times in one minute. If the velocity of sound is 360 m/s, find (i) frequency of the vibration in Hz, (ii) the wavelength of the sound produced.
(A) 120 Hz, 3 m
(B) 140 Hz, 3 m
(C) 120 Hz, 4 m
(D) 140 Hz,4 m

Answer 1

Hint: When a body vibrates then it undergoes to and fro motion and this is a type of periodic motion. Periodic motion has a time period which is defined as the time taken by the body to return to its initial position. Also, velocity, frequency and wavelength of a wave has a unique relationship among them.

Complete step by step answer:
Given quantities in the question are,
Vibrating 7200 times in one minute
One minute= 60 seconds
So, in 60 sec it vibrates 7200 times
In one sec= \[\dfrac{72000}{60}=120\]
Thus, the frequency is 120 Hz.
Now we are given the velocity, v=360 m/s
The relationship is given by \[v=f\times \lambda \]
Here f is the frequency and \[\lambda \]is the wavelength
Putting the values, \[360=120\times \lambda \]
So, \[\lambda \]=3 m
Thus, for the given wave the frequency is 120 Hz and the wavelength is 3 m.

Additional Information:
Frequency is the number of complete cycles per second for an oscillating body. It is the characteristic of the source and as the wave propagates through the medium it does not change. It is a constant. While other quantities like wavelength and velocity of the wave depends on the medium and changes.

Note:We need to keep in mind that all the units are in standard SI units. The wavelength to be taken in metre and velocity is m/s. The frequency is to be taken in Hertz (hz) or per second.