Question

A wave has a speed of 240 m/s and a wavelength of 3.2 m . What are the (a) frequency and (b) period of the wave?

Short answer

1. The frequency of the wave is 75 Hz .
2. The period of the wave is 13 ms.

Step-by-step solution

The given data

1. Speed of the wave, v = 240 m/s .
2. The wavelength of the wave, 13 ms .

Understanding the concept of wave

The transverse speed of the wave is the displacement of the wave in the given period of its oscillation, and the period is given by the reverse of the frequency of the wave. Thus, using the given formulae with the given data, the required values can be calculated.

Formulae:

The speed of the wave,

$v=f\lambda$ (i)

Where, f is the frequency and$\lambda$ is the wavelength of the wave.

The period of oscillation of the wave,

$T=\frac{1}{f}$ (ii)

a) Calculation of the frequency of the wave

Using the given data in equation (i), the frequency of the wave can be given as follows:

$$\begin{gathered} f=\frac{240\mathrm{m}/\mathrm{s}}{3.2\mathrm{m}} \\ =75\mathrm{Hz} \end{gathered}$$

Hence, the value of the frequency is 75 Hz .

b) Calculation of the period of the wave

Using the given data in equation (ii), the period of the oscillation can be given as follows:

$$\begin{gathered} T=\frac{1}{75\mathrm{Hz}} \\ =0.0133\mathrm{s} \\ =13.3\times {10}^{-3}\mathrm{s} \\ \approx 13\mathrm{ms} \end{gathered}$$

Hence, the value of the period is 13 ms .