Chapter 11, Problem 73GP

To determine

To calculate: The frequency of the sound wave.

Answer to Problem 73GP

The frequency of the sound wave $220\text{Hz}$ .

Explanation of Solution

Given:

Radius of the groove $r=10.8\text{cm}$

Angular velocity $\omega =33\text{rpm}$

Wavelength of the wave $\lambda =1.70\text{mm}$

Concept used:

Write the expression for speed of the wave.

  $v=f\lambda$

  $f=\frac{v}{\lambda }$

Also, $v=\frac{r}{\omega }$

By putting the value of $v$

  $f=\frac{r\omega }{\lambda }$

Here, $r$ Radius of the groove,

  $\omega$ is angular velocity,

  $\lambda$is the wavelength of the wave.

Calculation:

As $f=\frac{r\omega }{\lambda }$

by putting the values

  $f=\frac{0.108\text{m}\times 33\times 2\pi }{1.70\times {10}^{-3}\text{m}\times 60}$

  $f=220\text{Hz}$

Conclusion: The frequency of the sound wave $220\text{Hz}$ .