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Chapter 9: Problem 141

Change in temperature of the medium changes (A) frequency of sound waves. (B) amplitude of sound waves. (C) wavelength of sound waves. (D) loudness of sound waves.

Short Answer

Expert verified
A change in the temperature of the medium affects the speed of sound, which in turn affects the wavelength of sound waves according to the relation velocity = frequency x wavelength. Therefore, the correct answer is (C) wavelength of sound waves.

Step by step solution

01

Understanding the sound wave properties

A sound wave is a longitudinal wave that can travel through any medium, including solid, liquid, or gas. It is characterized by its frequency, amplitude, wavelength, and loudness. Let's briefly discuss each property. - Frequency: The number of oscillations (vibrations) per second that the particles in the medium make. It is measured in Hertz (Hz). - Amplitude: The maximum displacement of the particles in the medium from their equilibrium position. It is related to the energy of the wave and affects the loudness of the sound. - Wavelength: The distance between two consecutive points in the same phase of a wave, like two consecutive compressions or rarefactions. It is related to the speed of sound and frequency (velocity = frequency x wavelength). - Loudness: A subjective term that quantifies how strong a sound is perceived. It depends on the amplitude of the sound wave and the sensitivity of the listener's ear.
02

Identify the effect of the medium's temperature change on sound wave properties

Change in temperature affects the speed of sound in the medium as follows: Speed of sound in a gas = \(v = \sqrt{\gamma R T}\), where gamma is the adiabatic index, R is the molar gas constant, and T is the temperature of the medium in Kelvin. From this expression, we can see that the speed of sound in a medium is directly proportional to the square root of the temperature. Therefore, when the temperature of the medium changes, the speed of sound also changes.
03

Relate the speed of sound change to the changes in sound wave properties

As discussed earlier, the relationship between speed, frequency, and wavelength is: velocity = frequency x wavelength When the speed of sound changes due to a change in temperature, the wavelength will be affected. An increase in speed will result in an increase in wavelength, whereas a decrease in speed will result in a decrease in wavelength, provided that the frequency remains constant. The other properties, frequency, amplitude, and loudness, are not directly affected by the change in temperature of the medium.
04

Select the correct option

Based on the analysis above, we can conclude that a change in the temperature of the medium affects the wavelength of sound waves. Hence, the correct option is: (C) wavelength of sound waves.

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