Chapter 2: Q21DQ (page 497)
What is the purpose of the frets on a guitar? In terms of the frequency of the vibration of the strings, explain their use.
In string instruments like guitars, fret boards are used to play correct notes at right time by simply changing their pitch.
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As we discussed in Section 15.1, water waves are a combination of longitudinal and transverse waves. Defend the following statement: “When water waves hit a vertical wall, the wall is a node of the longitudinal displacement but an antinode of the transverse displacement.”
Two train whistles, A and B, each have a frequency of 393Hz. A is stationary and B is moving toward the right (away from A) at a speed of 35m/s. A listener is between the two whistles and is moving toward the right with a speed of 15m/s. No wind is blowing. (a) What is the frequency from A as heard by the listener? (b) What is the frequency from B as heard by the listener? (c) What is the beat frequency detected by the listener?
A musical interval of an octave corresponds to a factor of 2 in frequency. By what factor must the tension in a guitar or violin string be increased to raise its pitch one octave? To raise it two octaves? Explain your reasoning. Is there any danger in attempting these changes in pitch?
The intensity due to a number of independent sound sources is the sum of the individual intensities. (a) When four quadruplets cry simultaneously, how many decibels greater is the sound intensity level than when a single one cries? (b) To increase the sound intensity level again by the same number of decibels as in part (a), how many more crying babies are required?
Singing in the Shower. A pipe closed at both ends can have standing waves inside of it, but you normally don’t 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?
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