Chapter 9.2, Problem 10PP

To determine

To compare the wavelength in water to wavelength in air.

Answer to Problem 10PP

The wavelength in water is approximately $4.4$ times larger than in air.

Explanation of Solution

Given info:

Frequency of wave, $n=100.0\text{Hz}$

Speed of wave in water, $v_1=1500\text{m}/\text{s}$

Frequency of wave in air, $v_2=340\text{m}/\text{s}$

Formula used:

The speed of a wave is given by

  $v=n\lambda$

  $\lambda =\frac{v}{n}$

Calculation:

Let ${\lambda }_1$ is wavelength in water and ${\lambda }_2$ is wavelength in air. $v_1$ is speed of the wave in water and $v_2$ is speed of the wave in air.

  $\begin{array}{l}{\lambda }_1=\frac{v_1}{n}\\ {\lambda }_2=\frac{v_2}{n}\end{array}$

Where,

• ${\lambda }_1$is wavelength in water.
• ${\lambda }_2$is wavelength in air.

Substitute the given values in the above equation and calculate the wavelength in water.

  $\begin{array}{c}{\lambda }_1=\frac{1500}{100}\\ =15\text{Hz}\end{array}$

Substitute the given values in the above equation and calculate the wavelength in air.

  $\begin{array}{c}{\lambda }_2=\frac{340}{100}\\ =3.4\text{Hz}\end{array}$

Compare ${\lambda }_1$ and ${\lambda }_2$ .

${\lambda }_1=4.4{\lambda }_2$ .

Conclusion:

Therefore, the wavelength in water is $4.4$ times larger than in air.