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Chapter 17: Q. 75 (page 487)
Two loudspeakers emit 400 Hz notes. One speaker sits on the
ground. The other speaker is in the back of a pickup truck. You
hear eight beats per second as the truck drives away from you.
What is the truck’s speed?
This solution deals with the frequency and the beats per second
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As the captain of the scientific team sent to Planet Physics, one
of your tasks is to measure g. You have a long, thin wire labeled
1.00 g/m and a 1.25 kg weight. You have your accurate space cadet
chronometer but, unfortunately, you seem to have forgotten a
meter stick. Undeterred, you first find the midpoint of the wire by
folding it in half. You then attach one end of the wire to the wall
of your laboratory, stretch it horizontally to pass over a pulley at
the midpoint of the wire, then tie the 1.25 kg weight to the end
hanging over the pulley. By vibrating the wire, and measuring
time with your chronometer, you find that the wire’s second harmonic
frequency is 100 Hz. Next, with the 1.25 kg weight still
tied to one end of the wire, you attach the other end to the ceiling
to make a pendulum. You find that the pendulum requires 314 s to
complete 100 oscillations. Pulling out your trusty calculator, you
get to work. What value of g will you report back to headquarters?
Tendons are, essentially, elastic cords stretched between two fixed ends. As such, they can support standing waves. A woman has a 20-cm-long Achilles tendon—connecting the heel to a muscle in the calf—with a cross-section area of 90 mm2.. The density of tendon tissue is 1100 kg/m3. For a reasonable tension of 500 N, what will be the fundamental frequency of her Achilles tendon?
A manufacturing firm has hired your company, Acoustical Consulting, to help with a problem. Their employees are complaining about the annoying hum from a piece of machinery. Using a frequency meter, you quickly determine that the machine emits a rather loud sound at 1200 Hz. After investigating, you tell the owner that you cannot solve the problem entirely, but you can at least improve the situation by eliminating reflections of this sound from the walls. You propose to do this by installing mesh screens in front of the walls. A portion of the sound will reflect from the mesh; the rest will pass through the mesh and reflect from the wall. How far should the mesh be placed in front of the wall for this scheme to work?
Two radio antennas are separated by 2.0 m. Both broadcast
identical 750 MHz waves. If you walk around the antennas in a
circle of radius 10 m, how many maxima will you detect?
Two loudspeakers in a room emit 686 Hz sound waves
along the x-axis.
a. If the speakers are in phase, what is the smallest distance between the speakers for which the interference of the sound
waves is maximum destructive?
b. If the speakers are out of phase, what is the smallest distance
between the speakers for which the interference of the sound
waves is maximum constructive?
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