Question

A sound of waves produces $40$ crests and troughs in $0.4s$. What is the frequency of the wave?

Answer 1

Hint: The crest is the highest point of a wave's surface, whereas the trough is the lowest. The wave height is the vertical distance between the crest and the trough. The wavelength is the horizontal distance between two adjacent crests or troughs. The frequency, denoted by the Greek symbol nu ($\nu $), is the number of waves passing through a specific spot in a given amount of time. Frequency is usually expressed in cycles per second or waves per second. A Hertz is a unit of measurement for one wave per second (\[Hz\]).

Complete step by step solution:
One crest and one trough make up a complete cycle.
The supplied source generates \[40\] crests and \[40\] troughs, resulting in \[40\] wave cycles in the given 0.4 second interval.
A time period is the amount of time it takes for one cycle to complete.
And the time period of the given wave $ = $$\dfrac{{0.4s}}{{40}} = 0.01s$
As a result, the number of wave cycles generated in one second $ = $ $\dfrac{{40 \times 1}}{{0.4}}$$ = $$100$\[Hz\]
We know that the frequency is equal to the number of wave cycles produced in one second.
As a result, the required wave's frequency is $100$ \[Hz\].

Note: A disturbance or variation in a medium that carries energy from point to point and can take the form of an elastic deformation, a change in pressure, electric or magnetic intensity, electric potential, or temperature.