Question

The stationary waves are produced in a $20m$ long stretched string fixed at both ends. if the string vibrates in $10$ loops and the wave velocity in the string is $20m/s$, then the frequency of the wave is

Answer 1

Step 1: Given data

Length of a long stretched string fixed at both ends $=20\mathrm{m}$.

The number of loops $=10$.

Wave velocity in the string, $\mathrm{v}=20\mathrm{m}/\mathrm{s}$.

Step 2: Formula used

Calculate the frequency of the wave by using the formula below.

$\mathrm{v}=\lambda v...\left(1\right)$

Where, $\mathrm{v}$ is the velocity, $\lambda$ is the wavelength, and $\nu$ is the frequency of the wave.

Step 3: Calculation

There are $10$ loops in $20\mathrm{m}$

$\therefore$Length of one loop $=2\mathrm{m}$.

Length of two loops $=2x2=4\mathrm{m}$.

We know that, $\lambda =4\mathrm{m}$

Calculating the frequency of the wave using equation (1).

$\mathrm{v}=\lambda v$

$20=\nu \times 4$

$\nu =5\mathrm{Hz}$

Hence the frequency of the wave is $5Hz$.