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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

A soprano sings the note \(C 6(1046 \mathrm{~Hz})\) across the mouth of a soda bottle. To excite a fundamental frequency in the soda bottle equal to this note, describe how far the top of the liquid must be below the top of the bottle.

You are playing a note that has a fundamental frequency of \(400 .\) Hz on a guitar string of length \(50.0 \mathrm{~cm}\). At the same time, your friend plays a fundamental note on an open organ pipe, and 4 beats per seconds are heard. The mass per unit length of the string is \(2.00 \mathrm{~g} / \mathrm{m}\). Assume the velocity of sound is \(343 \mathrm{~m} / \mathrm{s}\). a) What are the possible frequencies of the open organ pipe? b) When the guitar string is tightened, the beat frequency decreases. Find the original tension in the string. c) What is the length of the organ pipe?

In a suspense-thriller movie, two submarines, \(X\) and Y, approach each other, traveling at \(10.0 \mathrm{~m} / \mathrm{s}\) and \(15.0 \mathrm{~m} / \mathrm{s}\), respectively. Submarine X "pings" submarine Y by sending a sonar wave of frequency \(2000.0 \mathrm{~Hz}\). Assume that the sound travels at \(1500.0 \mathrm{~m} / \mathrm{s}\) in the water. a) Determine the frequency of the sonar wave detected by submarine Y. b) What is the frequency detected by submarine \(X\) for the sonar wave reflected off submarine Y? c) Suppose the submarines barely miss each other and begin to move away from each other. What frequency does submarine Y detect from the pings sent by X? How much is the Doppler shift?

A policeman with a very good ear and a good understanding of the Doppler effect stands on the shoulder of a freeway assisting a crew in a 40 -mph work zone. He notices a car approaching that is honking its horn. As the car gets closer, the policeman hears the sound of the horn as a distinct \(\mathrm{B} 4\) tone \((494 \mathrm{~Hz}) .\) The instant the car passes by, he hears the sound as a distinct \(\mathrm{A} 4\) tone \((440 \mathrm{~Hz}) .\) He immediately jumps on his motorcycle, stops the car, and gives the motorist a speeding ticket. Explain his reasoning.

A thin aluminum rod of length \(L=2.00 \mathrm{~m}\) is clamped at its center. The speed of sound in aluminum is \(5000 . \mathrm{m} / \mathrm{s}\). Find the lowest resonance frequency for vibrations in this rod.
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