15 Traveling Waves and Sound

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• 15 Traveling Waves and Sound

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Example Problem
The water in the open ocean is in constant
motion, carrying long-wavelength waves moving at
relatively high speeds. Under steady winds, the
amplitude of these waves can get quite large.
Suppose a boat is at rest in the open ocean. The
wind has created a steady wave with wavelength
190 m traveling at 14 m/s. (In fact, the ocean
will support a mix of waves, but for steady winds
of 30-40 knots, this is the most prevalent
wavelength, and the correct speed for a wave of
this wavelength in deep water.) The top of the
crests of the waves is 2.0 m above the bottom of
the troughs. (This wave height is quite typical
for windy days in the Atlantic Ocean. The
Southern Ocean, with its planet-circling stretch
of open water, supports much larger waveswave
heights of 7 m are quite common.) What is the
maximum vertical speed of the boat as it bobs up
and down on the passing wave? What is the maximum
vertical acceleration?
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Energy and Intensity
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The Decibel Scale
Sound intensity level is measured in decibels.
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Example Problems
If you are standing 2.0 m from a lamp that is
emitting 100 W of infrared and visible light,
what is the intensity of radiation on your skin?
How does this compare with the intensity of
sunlight, approximately 1000 W/m2 at the surface
of the earth? Suppose it was so quiet outside
that you could detect a sound at the threshold of
your perception, 0 dB. Now suppose that someone
was playing a stereo with the volume cranked up
all the way. How far away could you detect the
sound from the stereo?
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Example Problem

• You are working in a shop where the noise level
  is a constant 90dB.
• Your eardrum has a diameter of approximately 8.4
  mm. How much power is being received by one of
  your eardrums?
• This level of noise is damaging over a long time,
  so you use earplugs that are rated to reduce the
  sound intensity level by
• 26 dB, a typical rating. What is the power
  received by one eardrum now?

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Example Problem
Your ears are, in principle, sensitive to sound
down to 0 dB. In practice, though, background
noise limits your threshold of hearing to about
20 dB. Suppose that someone is playing a stereo
with the volume cranked up all the way, giving a
sound intensity level of 110 dB at a distance of
1.0 m. How far away could you be and still hear
the music? That is, at what distance from the
stereo would the sound intensity level be 20 dB?
(This example is a bit artificial because loss
mechanisms work at these great distances and any
practical situation would involve reflections,
but it is instructive.)
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Additional Examples
A 5.0 kg block is hung from the ceiling on a
2.0-meter-long metal wire with a mass of 4 g. The
wire is plucked at the very bottom, where it
connects to the block. How long does it take the
pulse to reach the ceiling? The intensity of
sunlight is approximately 1000 W/m2 at the
surface of the earth. Saturn is about 10 times as
far from the sun as the earth. If the earth were
moved to the distance of Saturn, what would be
the intensity of sunlight at the surface? Suppose
you are powering a spacecraft with a 1.0 m2 array
of solar cells with an efficiency of 12. Above
the earths atmosphere, where the intensity of
sunlight is approximately 1300 W/m2, what is the
maximum power you could get from the solar cells?
How much power could you get if your spacecraft
was nearing Neptune, 30 times as far from the sun
as the earth?
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• 16 Superposition and Standing Waves

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Reading Quiz

• When two waves overlap, the displacement of the
  medium is the sum of the displacements of the two
  individual waves. This is the principle of
  __________.
• constructive interference
• destructive interference
• standing waves
• superposition

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Answer

• When two waves overlap, the displacement of the
  medium is the sum of the displacements of the two
  individual waves. This is the principle of
  __________.
• constructive interference
• destructive interference
• standing waves
• superposition

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Reading Quiz

• A point on a standing wave that is always
  stationary is a _________.
• maximum
• minimum
• node
• antinode

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Answer

• A point on a standing wave that is always
  stationary is a _________.
• maximum
• minumum
• node
• antinode

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Reading Quiz

• You can decrease the frequency of a standing wave
  on a string by
• making the string longer.
• using a thicker string.
• decreasing the tension.
• all of the above.

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Answer

• You can decrease the frequency of a standing wave
  on a string by
• making the string longer.
• using a thicker string.
• decreasing the tension.
• all of the above.

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