Chapter 13.4, Problem 51PPSE

Solution

To find: The equation for the given pitch.

  $y=\sin 240000\pi \theta$

Given:

The pitch $120000$ cycles per second and $a=1$

Concept used:

The sine function has the form $y=a\mathrm{sinb}\theta$ where $a=$ amplitude and $b=\frac{2\pi }{\text{period}}$

Calculation:

It is understood that $\text{period}=\frac{\text{seconds}}{\text{cycle}}$ So,

  $\text{period}=\frac{1}{120000}$

Therefore, the value of $b$ is,

  $\begin{array}{l}b=\frac{2\pi }{1/120000}\\ b=240000\pi \end{array}$

So, the function for the given pitch is,

  $y=\sin 240000\pi \theta$

Conclusion:

Hence, the equation for the pitch is $y=\sin 240000\pi \theta$