Sound 13-3

1
Sound13-3

• A physical phenomenon that stimulates the
• sense of hearing.

2
What do you think?

• A violin, a trumpet, and a clarinet all play the
  same note, a concert A. However, they all sound
  different.
• What is the same about the sound?
• Are the frequencies produced the same?
• Are the wave patterns the same?
• Why do the instruments sound different?

3
Standing Waves

• Standing waves are produced when two identical
  waves travel in opposite directions and
  interfere.
• Interference alternates between constructive and
  destructive.
• Nodes are points where interference is always
  destructive.
• Antinodes are points between the nodes with
  maximum displacement.

4
Standing Waves on a String

• There is a node at each end because the string is
  fixed at the ends.
• The diagram shows three possible standing wave
  patterns.
• Standing waves are produced by interference as
  waves travel in opposite directions after
  plucking or bowing the string.
• The lowest frequency (one loop) is called the
  fundamental frequency (f1).

5
Standing Waves on a String

• To the left is a snapshot of a single loop
  standing wave on a string of length, L.
• What is the wavelength for this wave?
• Answer ? 2L
• What is the frequency?
• Answer

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(No Transcript)
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Harmonics

• n is the number of loops or harmonic number.
• v is the speed of the wave on the string.
• Depends on tension and density of the string
• L is the length of the vibrating portion of the
  string.
• How could you change the frequency (pitch) of a
  string?

8
Fundamental Frequency
Click below to watch the Visual Concept.
Visual Concept
9
Standing Waves in an Air Column

• Wind instruments also use standing waves.
• Flutes, trumpets, pipe organs, trombones, etc.
• Some instruments have pipes open at both ends
  while others have one end closed.
• Air is free to move at open ends so antinodes
  occur.
• Closed ends are nodes.
• The velocity of the wave is now the velocity of
  sound in air (346 m/s at 25C).

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Both Ends Open
11
Closed at One End
12
Wind Instruments

• Wind instruments are not as simple as organ
  pipes.
• The shape is not always cylindrical.
• The holes change the wave patterns as well.
• The size of the pipe varies along the length.

13
Practice Problems

• One string on a toy guitar is 34.5 cm long.
• What is the wavelength of the first harmonic or
  the fundamental wavelength?
• Answer 69.0 cm or 0.690 m
• The string is plucked and the speed of the waves
  on the string is 410 m/s. What are the
  frequencies of the first three harmonics?
• 590 Hz, 1200 Hz, 1800 Hz
• Note The use of significant figures causes the
  multiples of 590 to be 1200 and 1800 because only
  two significant figures are present in the answer.

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Practice Problems

• An organ pipe open at both ends is 34.5 cm long.
• What is the wavelength of the first harmonic or
  the fundamental wavelength?
• Answer 69.0 cm or 0.690 m
• What are the frequencies of the first three
  harmonics if the air temperature is 25.0C?
• Answers 501 Hz, 1000 Hz, 1500 Hz
• Answer the same questions if the pipe is closed
  at one end.
• Answers 251 Hz, 753 Hz, 1250 Hz

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Practice Problems

• A violin string that is 50.0 cm long has a
  fundamental frequency of 440 Hz. What is the
  speed of the waves on this string?