Chapter 4, Problem 69RE

a.

To determine

The wave equation of the sound wave.

Answer to Problem 69RE

The wave equation $y=2\sin \left(528\pi x\right)$ .

Explanation of Solution

Given:

The function is given as:

  $\begin{array}{l}y=a\sin \left(bx\right)\\ \text{where,}\\ a=\text{amplitude}\\ x=\text{measured in seconds}\\ \text{time period:}\\ p=\frac{1}{264}\sec \end{array}$

For the sound wave where the amplitude is 2 and the period is $\frac{1}{264}$ seconds then it is given as:

  $\begin{array}{r}a=2\\ b=\frac{2\pi }{p}\\ =\frac{2\pi }{\frac{1}{264}}\\ =528\pi \end{array}$

Therefore, the wave equation $y=2\sin \left(528\pi x\right)$ .

b.

To determine

The frequency of the sound wave.

Answer to Problem 69RE

The wave frequency is 264 cycles/second.

Explanation of Solution

Given:

The function is given as:

  $\begin{array}{l}y=a\sin \left(bx\right)\\ \text{where,}\\ a=\text{amplitude}\\ x=\text{measured in seconds}\\ \text{time period:}\\ p=\frac{1}{264}\sec \end{array}$

For the sound wave where the amplitude is 2 and the period is $\frac{1}{264}$ seconds then it is given as:

  $\begin{array}{c}f=\frac{1}{p}\\ =\frac{1}{\frac{1}{264}}\\ =264\text{cycles/second}\end{array}$

Therefore, the wave frequency is 264 cycles/second.