Question

The relationship between frequency (f) and time period (T) is given by
A.$f=T$
B.$f=\dfrac{1}{T}$
C.$T={{f}^{2}}$
D.$T={{f}^{3}}$

Answer 1

Hint: We know that number of oscillations per second or repetitions per second is termed as frequency f of a wave but time period is the time taken to complete one oscillation or repetition so by using above two statements for frequency and time period we will derive a relation between frequency and time period.

Complete answer:
In wave motion particles move around the equilibrium position or mean position with some interval of time in which the particle oscillates between highest point(crest) and lowest point (trough) and time period is defined as to complete one such oscillation and is denoted by T.
Total number of oscillations (discussed above) in per unit time is known as frequency.
By the above two statements of frequency and time period we can observe that they are reciprocal to each other, as frequency is total oscillations in a unit time and time period is total time taken in one such oscillation so,
$\Rightarrow f=\dfrac{1}{T}$
Here, f (frequency of oscillation) and T (time period of oscillation).
$\therefore $The relationship between the frequency (f) and time period (T) is given by, $f=\dfrac{1}{T}$.

Hence option (B) is correct.

Note:
The unit of frequency is hertz (abbreviated as Hz) and 1Hz is equal to 1 cycle/sec or one oscillation per second. Sometimes students get confused in periodic and period, here periodic means when an event is repeating during some interval of time and period means that interval of time of periodic event. Frequency of a wave can vary in medium to medium and the range of frequency will solely depend on the total number of oscillations in that medium.