Question

The distance between one crest and one trough produced on the surface of the water is $0.04\mathrm{m}$. If the waves are produced at a rate of$180$ per minute. Calculate the wave velocity.

Answer 1

Step 1: Given data

Distance between one crest and trough, i.e. half the wavelength $\frac{\lambda }{2}=0.04m$ $\Rightarrow \lambda =0.08m$

Number of waves in $60$ second, $n=180$

Number of waves in 1 s, i.e. the frequency = $\frac{180}{60}=3persec$

Frequency, f = $3Hz$

Let us assume that $v$ is the speed of the wave.

Step 2: Formula used

Velocity of the wave $v=f\lambda$

Step 3: Solution

$v=f\lambda$

$\Rightarrow v=3\times 0.08$

$\Rightarrow v=0.24m/s$

The velocity of the wave is 0.24 m/s.