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Chapter 17: Q1 (page 482)
FIGURE Q17.1 shows a standing wave oscillating on a string at frequency f0. a. What mode (m-value) is this? b. How many antinodes will there be if the frequency is doubled to 2f0?
a) m = 4, This is a 4 modes wave.
b) There will be 8 antinodes if frequency is doubled.
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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 soap bubble is essentially a very thin film of water 1n = 1.332 surrounded by air. The colors that you see in soap bubbles are produced by interference.
a. Derive an expression for the wavelengths lC for which constructive interference causes a strong reflection from a soap bubble of thickness d. Hint: Think about the reflection phase shifts at both boundaries.
b. What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble? What color would such a soap bubble appear to be?
FIGURE EX17.3a is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. At what time was the snapshot graph in FIGURE EX17.3b taken?
When mass is tied to the bottom of a long, thin wire suspended from the ceiling, the wire's second-harmonic frequency isAdding an additionalto the hanging mass increases the second-harmonic frequency. What is ?
A violinist places her finger so that the vibrating section of a 1.0 g/m string has a length of 30 cm, then she draws her bow across it. A listener nearby in a 20°C room hears a note with a wavelength of 40 cm. What is the tension in the string?
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