Chapter 17, Problem 1ASA

To determine

The wave speed equation in relation to frequency andwave speed equation related to the period of oscillation.

Answer to Problem 1ASA

$\underset{\_}{\boxed{v=f\lambda }}$ is the wave speed equation in relation to frequency and wavelength and $\underset{\_}{\boxed{v=\frac{\lambda }{T}}}$ is the wave speed equation related to the period of oscillation.

Explanation of Solution

Write the expression for the wave speed in terms of frequency and wavelength.

  $v=f\lambda$        (I)

Here, $v$ is the wave speed, $f$ is the frequency, and $\lambda$ is the wavelength.

Write the expression for the frequency in terms of time period.

  $f=\frac{1}{T}$        (II)

Here, $T$ is the time period.

Conclusion:

Solve for $v$ using equations (I) and (II).

  $v=\frac{\lambda }{T}$        (III)

From the equation (I),

The wave speed is directly proportional to the frequency and wavelength.

From the equation (III),

The wave speed is the ratio of the wavelength to the time period of the wave.

Therefore, $\underset{\_}{\boxed{v=f\lambda }}$ is the wave speed equation in relation to frequency and wavelength and $\underset{\_}{\boxed{v=\frac{\lambda }{T}}}$ is the wave speed equation related to the period of oscillation.