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Chapter 2: Q8DQ (page 496)
For transverse waves on a string, is the wave speed the same as the speed of any part of the string? Explain the difference between these two speeds. Which one is constant?
The speed of the wave on the String is not the same as the speed of any other part of the string.
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Singing in the Shower. A pipe closed at both ends can have standing waves inside of it, but you normally don鈥檛 hear them because little of the sound can get out. But you can hear them if you are inside the pipe, such as someone singing in the shower. (a) Show that the wavelengths of standing waves in a pipe of length L that is closed at both ends are and the frequencies are given by , where n = 1, 2, 3, c.(b) Modelling it as a pipe, find the frequency of fundamental and the first two overtones for a shower 2.50 m tall. Are these frequencies audible?
BIO Audible Sound. Provided the amplitude is sufficiently great, the human ear can respond to longitudinal waves over a range of frequencies from about 20.0 Hz to about 20.0 kHz . (a) If you were to mark the beginning of each complete wave pattern with a red dot for the long-wavelength sound and a blue dot for the short-wavelength sound, how far apart would the red dots be, and how far apart would the blue dots be? (b) In reality would adjacent dots in each set be far enough apart for you to easily measure their separation with a meter stick? (c) Suppose you repeated part (a) in water, where sound travels at 1480 m/s . How far apart would the dots be in each set? Could you readily measure their separation with a meter stick?
The Vocal Tract. Many opera singers (and some pop singers) have a range of about octaves or even greater. Suppose a soprano鈥檚 range extends from A below middle C (frequency 220 Hz) up to E-flat above high C (frequency 1244 Hz). Although the vocal tract is quite complicated, we can model it as a resonating air column, like an organ pipe, that is open at the top and closed at the bottom. The column extends from the mouth down to the diaphragm in the chest cavity, and we can also assume that the lowest note is the fundamental. How long is this column of air if v = 354 m/s? Does your result seem reasonable, on the basis of observations of your own body?
(a) If two sounds differ by 5.00 dB, find the ratio of the intensity of the louder sound to that of the softer one. (b) If one sound is 100 times as intense as another, by how much do they differ in sound intensity level (in decibels)? (c) If you increase the volume of your stereo so that the intensity doubles, by how much does the sound intensity level increase?
A thin, 75.0cm wire has a mass of 16.5g. One end is tied to a nail, and the other end is attached to a screw that can be adjusted to vary the tension in the wire. (a) To what tension (in newtons) must you adjust the screw so that a transverse wave of wavelength 3.33 cm makes 625 vibrations per second? (b) How fast would this wave travel?
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