Chapter 9.6, Problem 12E

a

To determine

To find: A sinusoidal function and its graph for pressure P as a function of time $t$ (in sec).

Answer to Problem 12E

  $P=5\sin 880\pi t$

  

Explanation of Solution

Given information:

A vibration is produced using tuning fork. The maximum pressure produced from sound of frequency of $440$ Hz is $5$ minipascal.

Calculation:

The maximum pressure produced from sound of frequency of $440$ Hz is $5$ minipascal.

Model sinusoidal equation is given as-

  $P=a\sin bt$ .

Maximum pressure is $5$ . So, $a=5$ .

  $\begin{array}{l}\text{Also, frequency}=\frac{1}{\text{Period}}\\ \Rightarrow f=\frac{1}{\frac{2\pi }{b}}\\ \Rightarrow f=\frac{b}{2\pi }\\ \Rightarrow 440=\frac{b}{2\pi }\\ \Rightarrow b=880\pi \end{array}$

Thus, pressure $P$ as a function of time would be given as $P=5\sin 880\pi t$ .

Plotting the graph as below −