Chapter 16: Problem 54
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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Two vehicles carrying speakers that produce a tone of frequency \(1000.0 \mathrm{~Hz}\) are moving directly toward each other. Vehicle \(\mathrm{A}\) is moving at \(10.00 \mathrm{~m} / \mathrm{s}\) and vehicle \(\mathrm{B}\) is moving at \(20.00 \mathrm{~m} / \mathrm{s}\). Assume that the speed of sound in air is \(343.0 \mathrm{~m} / \mathrm{s},\) and find the frequencies that the driver of each vehicle hears.
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 \(1400 .\) Hz. Once it passes, the frequency is \(1200 .\) Hz. What is the actual frequency of the ambulance's siren?
Find the resonance frequency of the ear canal. Treat it as a half-open pipe of diameter \(8.0 \mathrm{~mm}\) and length \(25 \mathrm{~mm}\). Assume that the temperature inside the ear canal is body temperature \(\left(37^{\circ} \mathrm{C}\right)\).
If two loudspeakers at points \(A\) and \(B\) emit identical sine waves at the same frequency and constructive interference is observed at point \(C\), then the a) distance from \(A\) to \(C\) is the same as that from \(B\) to \(C\). b) points \(A, B,\) and \(C\) form an equilateral triangle. c) difference between the distance from \(A\) to \(C\) and the distance from \(B\) to \(C\) is an integer multiple of the wavelength of the emitted waves. d) difference between the distance from \(A\) to \(C\) and the distance from \(B\) to \(C\) is a half-integer multiple of the wavelength of the emitted waves.
A bugle can be represented by a cylindrical pipe of length \(L=1.35 \mathrm{~m} .\) The pipe is open at one end and closed at the other end (the end with the mouthpiece). Calculate the longest three wavelengths of standing waves inside the bugle. Also calculate the three lowest frequencies and the three longest wavelengths of the sound that is produced in the air around the bugle.
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