Chapter MPS, Problem 13.8MPS

a.

To determine

Find the period of the function.

Answer to Problem 13.8MPS

  $0.05\sec ond$

Explanation of Solution

Given information:

Goldfish can hear sound with lower frequency than humans can hear. Goldfish can hear as low as $20$ hertz, or $20$ cycles per second.

Calculation:

The goldfish can hear $20$ cycles per second.

This implies, the period is $\frac{1}{20}$ second.

That is, $0.05\sec ond$ .

Hence, the period of the function is $0.05\sec ond$ .

b.

To determine

Find the sine wave to represent the sound wave $y$ as a function of $t$ .

Answer to Problem 13.8MPS

  $y=\sin 40\pi$

Explanation of Solution

Given information:

Goldfish can hear sound with lower frequency than humans can hear. Goldfish can hear as low as $20$ hertz, or $20$ cycles per second.

Calculation:

The general form of sine wave is,

  $y=a\sin b\theta ,here,a=amplitude\&b=\frac{2\pi }{period}$ .

Substitute the value of $period=0.05$ and find $b$ as follows:

  $\begin{array}{l}b=\frac{2\pi }{period}\\ =\frac{2\pi }{0.05}\\ =20\times 2\pi \end{array}$

  $=40\pi$

So, substitute $a=1,\theta =t,andb=40\pi$ in equation $y=a\sin b\theta$ .

  $y=1\sin 40\pi t$

Hence, the sine wave to represent the sound wave $y$ as a function of $t$ is $y=\sin 40\pi$ .

c.

To determine

Plot a graph of $y=\sin 40\pi$ .

Answer to Problem 13.8MPS

  

Explanation of Solution

Given information:

Goldfish can hear sound with lower frequency than humans can hear. Goldfish can hear as low as $20$ hertz, or $20$ cycles per second.

Calculation:

The graph of the function $y=\sin 40\pi$ is as follows: