Question

The time period of a wave is $25\operatorname{s} $. What is the time required for the completion of \[150\] oscillations?

Answer 1

Hint: We know that the time period of an oscillatory system is defined as the time required to complete one oscillation. Thus, the time period given in the question is for one oscillation. To find the time required to complete \[150\] oscillations, we just have to use the unitary method to get the answer.

Complete step-by-step answer:
A crust and a trough together make one complete oscillation. The time taken by a wave to complete one oscillation is called the time period, often represented by $T$. From the question, we can infer that the time period of a wave is $25s$. This means it takes $25s$to complete one oscillation.
Now to find the total time taken to complete $150$ oscillations, we have to use the unitary method which is as follows:
Time required to complete $1$ oscillation$ = 25s$
Time required to complete $150$ oscillations$ = 25s \times 150$
Time required to complete $150$ oscillations$ = 3750s$
Therefore,$3750s$ which is approximately,$62.5$ minutes to complete $150$ oscillations.

Note: The reciprocal of the time period is known as frequency. Its S.I. unit is Hertz. The frequency is defined as the number of cycles or oscillations that are completed by a wave in one second.
The frequency can also be defined as the ratio of the speed of light and the wavelength of the wave. Mathematically represented by,
$c = \lambda \nu $
$ \Rightarrow \nu = \dfrac{c}{\lambda }$
Where,
$c$ is the speed of light.
$\lambda $ is the wavelength of the wave.
$\nu $ is the frequency of the wave.
As the speed of light is a constant quantity, we can deduce that the frequency and wavelength of a wave are inversely proportional to each other.