Chapter 4, Problem 69RE

To determine

To calculate: the equation of sound wave and its frequency.

Answer to Problem 69RE

The equation of sound wave is $y=2\sin 528\pi x$

The frequency of sound wave is $264cycle/\sec ond$ .

Explanation of Solution

Given information:

Given equation is $y=a\sin bx$

Where x is measured in second,a is amplitude which is equal to $2$ and b is period which is $\frac{1}{264}per\sec ond$ .

Formula used:time period is $T=\frac{1}{f}$

Where f is frequency,T is time period.

Also,wavelength of $1$ cycle is $2\pi$ .

Calculation:

Consider the statement “equation of sound wave and its frequency.”.

Recall that, $T=\frac{1}{f}$

Where f is frequency,T is time period.

Therefore, $\frac{1}{264}=\frac{1}{frequency}$

Therefore, $frequency=264cycleper\sec ond$

Recall that wavelength is $2\pi per\sec ond$

Therefore, $\begin{array}{l}b=f*2\pi \\ b=264*2\pi \\ b=528\pi \end{array}$

Where b is period and f is frequency

Therefore, the equation of sound wave is

  $y=2\sin 528\pi x$

And frequency is $264cycle/\sec ond$ .