Chapter 15, Problem 75A

a.

To determine

To Explain: The way through which frequency will change if pitch is increased.

Explanation of Solution

Introduction:

Frequency is related to pitch.Frequency refers to the number of times sound waves pass through a certain point in a second. Pitch is described as the sensation of frequency.

A high-pitched frequency is produced by a sound of high frequency whereas a low-pitched sound is produced by a low frequency sound wave. Therefore, if the pitch is increased, the frequency will also increase.

Conclusion:

Frequency will increase if pitch is increased.

b.

To determine

To Explain: Whether wavelength will change if pitch is increased.

Explanation of Solution

Introduction:

Wavelength is given by the formula:

  $\lambda =\frac{v}{f}$

Where, $v$ is velocity and $f$ is frequency.

Assuming velocity to be constant in the formula- $\lambda =v/f$ . Therefore,

  $\lambda \propto \frac{1}{f}$

Frequency and wavelength is inversely proportional. Since frequency is related to the pitch of a sound, pitch and wavelength will also be inversely proportional. Therefore, if pitch is increased, wavelength will decrease.

Conclusion:

Wavelength will decrease, if pitch is increased.

c.

To determine

To Explain: The way through which wave velocity will change if pitch is increased.

Explanation of Solution

Introduction:

Wave velocity refers to the speed of a wave in a particular direction. It is given by the formula:

  $v=\lambda f$

Where, $\lambda$ is wavelength and $f$ is frequency.

For one particular medium, the speed of waves will always remain constant with increasing or decreasing frequencies. Since frequency is referred to as pitch, an increase in pitch will not affect the speed of the wave.

Conclusion:

Wave velocity will remain same if pitch is increased.

d.

To determine

To Explain: The way through which amplitude will change if pitch is increased.

Explanation of Solution

Introduction:

Amplitude of a wave refers to the maximum displacement of a particle on either side of its mean position.

The displacement of particles on either side of its mean position(amplitude) will not vary according to the number of waves passing through a particular point in a second(frequency). Since frequency is referred to as pitch, therefore, if pitch is increased, the amplitude will remain the same.

Conclusion:

Amplitude will remain same if pitch is increased.