Question

Find the time period of a wave whose frequency is 400 Hz?
A. 0.0012 s
B. 0.0025 s
C. 0.0015 s
D. 0.0010 s

Answer 1

Hint: Time period of anything is the amount of time required for it to complete one oscillation. Usually when we have angular velocity we can get frequency from it and when we get frequency the inverse of that frequency gives us the time period.
Formula used:
$T={\displaystyle \frac{1}{f}}$

Complete answer:
There are two kinds of waves normally. One will be a transverse wave and the other will be a longitudinal wave. In case of transverse waves the direction of propagation of waves is perpendicular to the direction of vibration of the particles of the medium. Transverse wave has crests and troughs.
In case of the longitudinal wave particles of the medium of propagation vibrates in the direction of propagation of the wave. This longitudinal wave has compressions and rarefactions. In case of longitudinal waves particles vibrate in to and fro motion. Transverse waves can propagate without medium too whereas longitudinal waves require medium to propagate. Example for transverse wave is light whereas example for the longitudinal wave is sound.
Frequency is the number of waves passing through a point within one second. If we take inverse of that frequency, we will get the time period.
If we have a transverse wave then in one time period one crest and trough passes through a particular point. If they give longitudinal waves then in one time period one compression and rarefaction passes through a point.
So time period(T) is given in terms of frequency as
$T={\displaystyle \frac{1}{f}}$
$\begin{array}{rl}& \Rightarrow T={\displaystyle \frac{1}{400}}\\ & \Rightarrow T=0.0025\sec \end{array}$
So the time period is 0.0025 seconds.

So, the correct answer is “Option B”.

Note:
Sometimes we might be asked to find out the time period when angular velocity was given, then we have to convert angular velocity into frequency by dividing the angular velocity with $2\pi$ to get the frequency and then find out the time period in the same way.