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
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You are driving along a highway at \(30.0 \mathrm{~m} / \mathrm{s}\) when you hear a siren. You look in the rear-view mirror and see a police car approaching you from behind with a constant speed. The frequency of the siren that you hear is \(1300 \mathrm{~Hz}\). Right after the police car passes you, the frequency of the siren that you hear is \(1280 \mathrm{~Hz}\). a) How fast was the police car moving? b) You are so nervous after the police car passes you that you pull off the road and stop. Then you hear another siren, this time from an ambulance approaching from behind. The frequency of its siren that you hear is \(1400 \mathrm{~Hz}\). Once it passes, the frequency is \(1200 \mathrm{~Hz}\). What is the actual frequency of the ambulance's siren?
Standing on the sidewalk, you listen to the horn of a passing car. As the car passes, the frequency of the sound changes from high to low in a continuous manner; that is, there is no abrupt change in the perceived frequency. This occurs because a) the pitch of the sound of the horn changes continuously. b) the intensity of the observed sound changes continuously. c) you are not standing directly in the path of the moving car. d) of all of the above reasons.
Compare the intensity of sound at the pain level, \(120 \mathrm{~dB}\), with that at the whisper level, \(20 \mathrm{~dB}\).
When two pure tones with similar frequencies combine to produce beats, the result is a train of wave packets. That is, the sinusoidal waves are partially localized into packets. Suppose two sinusoidal waves of equal amplitude A, traveling in the same direction, have wave numbers \(\kappa\) and \(\kappa+\Delta \kappa\) and angular frequencies \(\omega\) and \(\omega+\Delta \omega\), respectively. Let \(\Delta x\) be the length of a wave packet, that is, the distance between two nodes of the envelope of the combined sine functions. What is the value of the product \(\Delta x \Delta \kappa ?\)
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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