Chapter 17: 2. (page 482)
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?
All the energy at those instants is in the form of Kinetic energy.
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FIGURE Q17.8 is a snapshot graph of two plane waves passing
through a region of space. Each wave has a 2.0 mm amplitude
and the same wavelength. What is the net displacement of the
medium at points a, b, and c?
The lowest note on a grand piano has a frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 400 g. The vibrating section of the string is 1.90 m long. What tension is needed to tune this string properly?
Piano tuners tune pianos by listening to the beats between the
harmonics of two different strings. When properly tuned, the note
A should have a frequency of 440 Hz and the note E should be
at 659 Hz.
a. What is the frequency difference between the third harmonic
of the A and the second harmonic of the E?
b. A tuner first tunes the A string very precisely by matching it to
a 440 Hz tuning fork. She then strikes the A and E strings simultaneously
and listens for beats between the harmonics. What
beat frequency indicates that the E string is properly tuned?
c. The tuner starts with the tension in the E string a little low,
then tightens it. What is the frequency of the E string when
she hears four beats per second?
A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s. If the string’s linear density is 0.600 g/m and the tension is 150 N, how long is the vibrating section of the violin string?
Two in-phase loudspeakers emit identical 1000 Hz sound waves along the x-axis. What distance should one speaker be placed behind the other for the sound to have an amplitude 1.5 times that of each speaker alone?
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