Question

A wave source produces 10 oscillations in 100 ms. Find the time period of the wave.
A. 1 second
B. 0.01 second
C. 10 second
D. 0.1 second

Answer 1

Hint: The above problem can be solved by using the concept of the oscillatory motion. The oscillatory motion is defined as the motion of the particle about the mean position with a regular time interval. The duration in which the particle repeats its motion is called the time period of the motion.

Complete step by step answer:
Given: The number of oscillations of the wave source is $n = 10$, the time for completion of the oscillations is $t = 100\;{\text{ms}} = 100\;{\text{ms}} \times \dfrac{{{{10}^{ - 3}}\;{\text{s}}}}{{1\;{\text{ms}}}} = 0.1\;{\text{s}}$.
The formula to find the time period of the wave is given as:
$T = \dfrac{t}{n}$
Substitute 10 for n and 0.1 s for t in the above expression to find the time period of the wave.
$T = \dfrac{{0.1\;{\text{s}}}}{{10}}$
$\therefore T = 0.01\;{\text{s}}$

Thus, the time period of the wave is $0.01\;{\text{s}}$ and the option (B) is the correct answer.

Additional Information:
The number of oscillations per second is called the frequency of the wave. The frequency of the wave is inverse of the time period. If the particle repeats its motion in circular motion then the frequency is called the angular frequency. The distance covered by the particle in one time period is called the wavelength of the particle. The wavelength of the particle increases then the frequency of the particle decreases.

Note: The time period is also the same as the time to complete one oscillation of the motion. Convert the time for 10 oscillations from millisecond to second to find the time period of the wave. The time taken by the particle to cover the distance equal to wavelength is also called the time period.