Question

The product of the time period of a wave and its frequency is
A. infinity
B. zero
C. more than unity but less than infinity
D. unity

Answer 1

Hint: The time taken by the wave to cover one cycle is time period. The distance travelled by the wave in one cycle is wavelength.

Complete step by step solution:
 Time period of a wave: The time taken for one complete oscillation in the density of the medium is called the time period of the wave. It can also be defined as the time taken by two consecutive compressions (Trough) or rarefactions (Crest) to cross a fixed point. It is represented by the symbol T. Its unit is in second.

Frequency: The number of oscillations per unit time is called the frequency of the wave. The number of compressions (Trough) or rarefactions (Crest) that cross a given point in per unit time is the frequency of the wave. It is donated by f and its unit is hertz. Now, the time period of the wave in terms of wavelength $\left(\lambda \right)$and wave velocity (v) is given by, $T={\displaystyle \frac{\lambda }{v}}......\left(i\right)$ and that of the frequency is given by,
$f={\displaystyle \frac{v}{\lambda }}.....\left(ii\right)$
Multiplying the equation (i) and (ii)
$f\times T={\displaystyle \frac{v}{\lambda }}\times {\displaystyle \frac{\lambda }{v}}$
$f\times T=1$

Hence, option (D) is correct.

Additional Information: The slope of the graph between displacements versus time graph gives wave velocity.

Note: The ratio of wavelength $\left(\lambda \right)$ with wave velocity (v) is time period so $T={\displaystyle \frac{\lambda }{v}}$ and the ratio wave velocity (v) with wavelength $\left(\lambda \right)$ is frequency $f={\displaystyle \frac{v}{\lambda }}$.