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Chapter 17: Q. 37 (page 484)
A string vibrates at its third-harmonic frequency. The amplitude at a point 30 cm from one end is half the maximum amplitude. How long is the string?
The length of the string is 5.40 m
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Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by fn+1 = r fn for all n. In this system, the frequency doubles every 12notes鈥攁n interval called an octave.
a. What is the value of r?
b. Orchestras tune to the note A, which has a frequency of440 Hz. What is the frequency of the next note of the scale (called A-sharp)?
A 75 g bungee cord has an equilibrium length of 1.20 m. The
cord is stretched to a length of 1.80 m, then vibrated at 20 Hz. This
produces a standing wave with two antinodes. What is the spring
constant of the bungee cord?
If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat. What has happened to the energy of the wave at those instants?
Microwaves pass through a small hole into the 鈥渕icrowave cavity鈥� of FIGURE EX17.13. What frequencies between 10 GHz and 20 GHz will create standing waves in the cavity?
The 40-cm-long tube of FIGURE P17.54 has a 40-cm-long insert
that can be pulled in and out. A vibrating tuning fork is held next to the
tube. As the insert is slowly pulled out, the sound from the tuning fork
creates standing waves in the tube when the total length L is 42.5 cm, 56.7 cm, and 70.9 cm. What is the frequency of the tuning fork? Assume vsound = 343 m/s.
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