Question

A wave completes 20 vibrations in 2.5 s. Its frequency is:
A. 20 Hz
B. 8 Hz
C. 200 Hz
D. 50 Hz

Answer 1

Hint: One hertz equals one vibration per sec. The wave completes 20 vibrations in 2.5 s. Using this value, we have to find the number of vibrations per second by dividing the number of vibrations by the time taken. The frequency of the wave equals the number of vibrations per second.
Formula used:
\[1\,H=1{\text{vibration}}/{s}\;\]

Complete answer:
From the given information, we have the data as follows.
A wave completes 20 vibrations in 2.5 s.
Now we have to find the total number of vibrations per second. To do so, we have to divide the number of vibrations by the time taken. So, we have,
\[\begin{align}
  & 2.5\,s=20\,\text{vibrations} \\
 & \Rightarrow \text{1}\,\text{s}=\dfrac{20}{2.5}\text{vibrations} \\
\end{align}\]
Thus, the frequency of the wave is given as follows.
\[\begin{align}
  & f=\dfrac{20}{2.5}\text{vibrations} \\
 & \therefore f=8\,Hz \\
\end{align}\]

Additional information:
The definitions of the parameters related to the wave are as follows.

Time period: The time taken by a wave to complete one cycle is called the time period of a wave.
Frequency: The number of cycles that are completed in a certain amount of time is called the frequency of a wave.
Crest – A point on the wave with a maximum value of the amplitude or with the maximum displacement value is called the crest.
Through – A point on the wave with a minimum value of the amplitude or with the minimum displacement value is called the trough.
Wavelength: The distance between the successive crests or the troughs is called the wavelength.
\[\therefore \] The frequency of a wave that completes 20 vibrations in 2.5 s is 8 Hz.

Thus, option (B) is correct.

Note:
The frequency in terms of the vibrations can be defined as, “The number of vibrations per second is called the frequency.” The frequency is the number of cycles per second, whereas, the wavelength is meters per cycle.