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?
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.
An open-open organ pipe is 78.0 cm long. An open-closed pipe has a fundamental frequency equal to the third harmonic of the open-open pipe. How long is the open-closed pipe?
FIGURE EX17.1 is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. Draw six snapshot graphs, stacked vertically, showing the string at 1 s intervals from t = 1 s to t = 6 s
When mass M is tied to the bottom of a long, thin wire suspended
from the ceiling, the wire’s second-harmonic frequency is
200 Hz. Adding an additional 1.0 kg to the hanging mass increases
the second-harmonic frequency to 245 Hz. What is M?
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