Question

The wavelength of waves produced on the surface of water is 20 cm. If the wave velocity is 24 m $s^{-1}$, calculate the time in which one wave is produced ?

• A. $7.3\times {10}^{-3}s$
• B. $8.33\times {10}^{-2}s$
• C. $8.33\times {10}^{-3}s$
• D. $7\times {10}^{-3}s$

Answer 1

Answer: (C)

$8.33\times {10}^{-3}s$

In the question, the wavelength $\left(\lambda \right)$ is given as $20cm$, that is, $0.20m$ and the wave velocity, $v$ is given as $24$ $m/s$.
The frequency $\nu$, velocity $v$ and wavelength $\lambda$ relation is given as:
$\nu =\frac{v}{\lambda }$.
Number of waves produced in one second is called as frequency, i.e. $\nu =\frac{v}{\lambda }$ $=\nu =\frac{24}{0.20}$ $=120$ waves per second.
Time period of a wave is given as the inverse of frequency.

That is, $T=\frac{1}{\nu }$ $=\frac{1}{120}$ $=8.33\times {10}^{-3}seconds$
Hence, the time period of the wave is given as $8.33\times {10}^{-3}seconds$.