Question

A leopard leaps a distance of 1 meter in a straight line, 20 times in 1 minute, while catching a prey, then
A) The time period and frequency cannot be determined, since the leopard is not returning to its original position.
B) The product of its time period and frequency will be unity.
C) The time period is infinity.
D) The frequency is zero.

Answer 1

Hint: The time period is the total time taken by the wave to complete the motion of a wave. The frequency is the number of rotations in one complete cycle. The wavelength is the distance between the two consecutive crests or the distance between the consecutive troughs of a wavelength.

Complete step by step answer:
We can consider one by one each option and see which one is the correct answer to this problem.
Option A:
The time period and frequency cannot be determined, since the leopard is not returning to its original position. In this option, it is said that we cannot find the frequency but we find the frequency of the leopard is $\dfrac{1}{{20}}$, and the time period is 3seconds. So we can calculate the time period and frequency of the leopard and therefore the option A is not the correct answer for this problem.
Option B:
The frequency is equal $v$ and the time period is given by T. Now the frequency is nothing but the reciprocal of the time period of a particular wave so the product of frequency and time period is always unity. So option B would be the correct answer to this problem.
Option C:
The time period is infinity. The time period will be infinity only if the frequency is equal to zero as the time period is equal to $T = \dfrac{1}{v}$ where $v$ is the frequency of the wave which is not in this case the correct answer for this problem is not option C.
Option D:
The frequency is zero. The frequency of the motion of the leopard is not equal to zero. As the leap of the leopard’s leg can be considered as the frequency in 1 minute. So option D is also not the correct answer to this problem.

So after considering all the options the correct answer for this problem is option B.

Note:
The inverse of time taken is known as time period in the wave motion. The leap of the leopard motion can be considered here and not the whole motion of the leopard. As the frequency is the number of rotations in 1 minute and here the total time is 1 min. Therefore the number of leap’s can tell us about the frequency of the leopard.