Question

A source of wave produces $40$ crests and $40$ troughs in $0.4$ second. Find the frequency of the wave:
A. $50\,Hz$
B. $80\,Hz$
C. $100\,Hz$
D. $200\,Hz$

Answer 1

Hint: In order to solve this question, firstly we should know about the term frequency of a wave. Frequency is the number of oscillations of a wave in one second and here we will first determine the number of wave cycles produced in one second by using given information and then determine the frequency of the wave.

Complete step by step answer:
It is given to us that a source of wave produces $40$ crests and $40$ troughs in $0.4$ second and since crest is the point of a wave representing maximum amplitude of the wave whereas trough is just opposite of the crest in opposite direction. Since, we know that one complete cycle of a wave contains only one crest and one trough.

So, according to the question, the number of waves in one second can be calculated as $\dfrac{{40}}{{0.4}}=100$ and since, this is the number of waves cycle produced in one second and this represents the frequency of the wave.So, the source of wave which produces $40$ crests and $40$ troughs in $0.4$ second has the frequency of $100Hz$.

Hence, the correct option is C.

Note: It should be remembered that frequency is also defined as the reciprocal of the time period of a wave and its fundamental unit is known as Hertz or represented as ${\sec ^{ - 1}}$ denoted by Hz. Most commonly, the words crest and trough are used in case of sound waves.