Question

The disc of a siren containing 60 holes rotates at a constant speed of 360rpm. The emitted sound is in unison with a tuning fork of frequency
A. 10Hz
B. 360Hz
C. 216Hz
D. 60Hz

Answer 1

Hint: The number of revolutions taking place in one minute is given in the question, from that you could find the number of revolutions in one second. Since the disc of the siren has 60 holes on it, 60 waves will be produced at the end of one revolution. Now you could multiply the number of revolutions in one second with 60 to get the number of waves produced per second and hence the frequency of the tuning fork that is in unison with the siren.

Complete answer:
In the question, we are given a disc of a siren that consists of 60 holes on it. This disc of sirens is rotating at a constant speed of 360 revolutions per minute. We are asked to find the frequency of the tuning fork that is in unison with the emitted sound. So,
The number of revolutions per minute = 360
Number of seconds in a minute = 60
Therefore, the number of revolutions per second = $\dfrac{360}{60}=6$
So, there are 6 revolutions taking place in total in one second.
Since the given disc has 60 holes on it, on one complete revolution it will produce 60 sound waves.
We know that frequency is defined as the number of waves produced in one second. As there are 6 revolutions in a second, the number of waves produced in one second will be 6 times that produced in one revolution. So the number of sound waves produced in one second will be 360 waves.
Therefore, we found the frequency of the tuning fork that is in unison with the sound waves produced in the siren to be 360Hz. Hence, option B is the right answer.

Note:
We could call revolutions per minute or rpm as the unit of rotational speed or that of the frequency of rotation around a fixed axis. As discussed in the solution, rpm is the number of turns taking place in one minute. However, as per SI units, rpm is not considered as a unit but just as a semantic annotation.