Question

The waves produced by a pendulum, having time period 2 seconds are:
(A) Infrasonic
(B) Audible
(C) Ultrasonic
(D) None of these

Answer 1

Hint
The time period of the pendulum is given to be 2s. From this we can find the frequency of its wave. Since, ${\text{frequency = }}\dfrac{{\text{1}}}{{{\text{time period}}}}$
The frequency range for different types of waves is:
Infrasonic – less than $20Hz$
Audible - $20Hz{\text{ }}to{\text{ }}20,000Hz$
Ultrasonic – greater than $20,000Hz$
Find the frequency of the given pendulum and check in which category it falls.

Complete step by step answer
The TO and FRO motion of a pendulum is a type of periodic motion.
When the pendulum moves from its mean position to extreme position and comes back and goes to another extreme end and at last comes back to the mean position, we say one oscillation is complete. Time period is the time taken by a body to complete one oscillation.
Here, in the question it is given that the time period of the pendulum is 2 seconds.
Now, there is another term related to waves called frequency.
Frequency represents the no. of oscillations completed by a body in 1 second.
It is just the reciprocal of the time period:
${\text{frequency = }}\dfrac{{\text{1}}}{{{\text{time period}}}}$
In, the given question the frequency of the waves produced by the pendulum will be:
$frequency = \dfrac{1}{2} = 0.5{\text{ cycles/sec or Hz}}$
Now, Infrasonic waves are those waves which have frequency less than$20Hz$.
The range of frequency of audible sound waves is from$20Hz{\text{ }}to{\text{ }}20,000Hz$.
Waves with frequency higher than $20,000Hz$ are called ultrasonic waves.
Since, the given pendulum has frequency $0.5Hz{\text{ }}\left( { < 20Hz} \right)$.
Therefore, it produces infrasonic waves.

Note
Before finding frequency, by taking reciprocal of time period, always change the unit of time period to its SI unit i.e. seconds.