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Chapter 16: Problem 7

What has the greatest effect on the speed of sound in air? a) temperature of the air b) frequency of the sound c) wavelength of the sound d) pressure of the atmosphere

Short Answer

Expert verified
Answer: a) temperature of the air

Step by step solution

01

Consider the properties of sound

A sound wave is a mechanical wave that propagates through a medium, such as air, by compressing and rarefying the molecules of the medium. The speed of sound depends on the properties of the medium it travels through, and in this case, we are focusing on air.
02

Understanding the speed of sound in air

The speed of sound in air can be calculated using the following formula: \(v = \sqrt{\frac{\gamma R T}{M}}\) where \(v\) is the speed of sound, \(\gamma\) is the adiabatic index (ratio of specific heats), \(R\) is the gas constant, \(T\) is the absolute temperature, and \(M\) is the molar mass of the gas. From this formula, we can see that the speed of sound in air depends on the temperature (\(T\)) and the properties of the medium (the constants \(\gamma\), \(R\), and \(M\)).
03

Analyzing the effect of temperature on the speed of sound

As the temperature of the air increases, the speed of sound also increases. This relationship can be understood intuitively as the increased temperature leads to more energy for the air molecules, resulting in faster movement and better transmission of the sound wave.
04

Analyzing the effect of frequency and wavelength on the speed of sound

Frequency and wavelength are related to speed, but they do not directly affect the speed of sound in a medium. The relationship between speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) can be expressed as: \(v = f \lambda\) While frequency and wavelength do influence the speed of sound, they are more related to the properties of individual sound waves, not the overall speed of sound transmission in a medium.
05

Analyzing the effect of pressure on the speed of sound

In an ideal gas, the speed of sound does not depend on the pressure of the atmosphere. Although air is not an ideal gas, the variation in speed due to pressure changes is minimal compared to the effect of temperature. After analyzing each option, we can conclude that the greatest effect on the speed of sound in air is from: a) temperature of the air

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Most popular questions from this chapter

Two people are talking at a distance of \(3.0 \mathrm{~m}\) from where you are, and you measure the sound intensity as \(1.1 \cdot 10^{-7} \mathrm{~W} / \mathrm{m}^{2}\). Another student is \(4.0 \mathrm{~m}\) away from the talkers. What sound intensity does the other student measure?

A police siren contains at least two frequencies, producing the wavering sound (beats). Explain how the siren sound changes as a police car approaches, passes, and moves away from a pedestrian.

At a state championship high school football game, the intensity level of the shout of a single person in the stands at the center of the field is about \(50 \mathrm{~dB}\). What would be the intensity level at the center of the field if all 10,000 fans at the game shouted from roughly the same distance away from that center point?

A sound level of 50 decibels is a) 2.5 times as intense as a sound of 20 decibels. b) 6.25 times as intense as a sound of 20 decibels. c) 10 times as intense as a sound of 20 decibels. d) 100 times as intense as a sound of 20 decibels. e) 1000 times as intense as a sound of 20 decibels.

Electromagnetic radiation (light) consists of waves. More than a century ago, scientists thought that light, like other waves, required a medium (called the ether) to support its transmission. Glass, having a typical mass density of \(\rho=2500 \mathrm{~kg} / \mathrm{m}^{3},\) also supports the transmission of light. What would the elastic modulus of glass have to be to support the transmission of light waves at a speed of \(v=2.0 \cdot 10^{8} \mathrm{~m} / \mathrm{s} ?\) Compare this to the actual elastic modulus of window glass, which is \(5 \cdot 10^{10} \mathrm{~N} / \mathrm{m}^{2}\).
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