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Chapter 17: Q6. (page 482)
A flute filled with helium will, until the helium escapes, play notes at a much higher pitch than normal. Why?
Speed of sound is higher in helium than air.
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Standing waves on a 1.0-m-long string that is fixed at both ends are seen at successive frequencies of 36 Hz and 48 Hz. a. What are the fundamental frequency and the wave speed? b. Draw the standing-wave pattern when the string oscillates at 48 Hz.
Deep-sea divers often breathe a mixture of helium and oxygen to avoid getting the “bends” from breathing high-pressure nitrogen. The helium has the side effect of making the divers’ voices sound odd. Although your vocal tract can be roughly described as an open-closed tube, the way you hold your mouth and position your lips greatly affects the standing-wave frequencies of the vocal tract. This is what allows different vowels to sound different. The “ee” sound is made by shaping your vocal tract to have standing- wave frequencies at, normally, 270 Hz and 2300 Hz. What will these frequencies be for a helium-oxygen mixture in which the speed of sound at body temperature is 750 m/s? The speed of sound in air at body temperature is 350 m/s.
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?
Two loudspeakers emit sound waves of the same frequency along the x-axis. The amplitude of each wave is a. The sound intensity is minimum when speaker 2 is 10 cm behind speaker 1. The intensity increases as speaker 2 is moved forward and first reaches maximum, with amplitude 2a, when it is 30 cm in front of speaker 1. What is
a. The wavelength of the sound?
b. The phase difference between the two loudspeakers?
c. The amplitude of the sound (as a multiple of a) if the speakers
are placed side by side?
In a laboratory experiment, one end of a horizontal string is tied
to a support while the other end passes over a frictionless pulley
and is tied to a 1.5 kg sphere. Students determine the frequencies
of standing waves on the horizontal segment of the string, then
they raise a beaker of water until the hanging 1.5 kg sphere is
completely submerged. The frequency of the fifth harmonic with
the sphere submerged exactly matches the frequency of the third
harmonic before the sphere was submerged. What is the diameter
of the sphere?
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