Chapter 15.1, Problem 7SSC

To determine

To Draw: The graph of the displacement of the eardrum versus time for the two cycles.

Explanation of Solution

Given:

Frequency

  $f_1=1\text{ kHz}$

  $f_2=2\text{ kHz}$

Formula used:

Time period $T=\frac{1}{f}$

Where,

  $f$ is the frequency for the wave

Calculation:

Time period for the wave having frequency $f_1=1\text{ kHz}$ can be calculated as:

  $\begin{array}{l}T=\frac{1}{f}\\ T=\frac{1}{1000\text{ Hz}}\\ T={10}^{-3}\text{ s}\\ T=1\text{ms}\end{array}$

Displacement versus time graph for the wave having frequency $f_1=1\text{ kHz}$ can be drawn as:

  

Time period for the wave having frequency $f_2=2\text{ kHz}$ can be calculated as:

  $\begin{array}{l}T=\frac{1}{f}\\ T=\frac{1}{2000\text{ Hz}}\\ T=0.5\times {10}^{-3}\text{ s}\\ T=0.5\text{ms}\end{array}$

Displacement versus time graph for the wave having frequency $f_2=2\text{ kHz}$ can be drawn as:

  

Conclusion:

  $1\text{ms}$ is the time period of the wave having frequency $f_1=1\text{ kHz}$

  $0.5\text{ms}$ is the time period of the wave having frequency $f_2=2\text{ kHz}$