Sound 13 3
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Sound 13-3. A “physical phenomenon that stimulates the sense of hearing.”. 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?

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Sound 13-3

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Sound 13 3

Sound13-3

A “physical phenomenon that stimulates the

sense of hearing.”


What do you think

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?


Standing waves

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.


Standing waves on a string

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).


Standing waves on a string1

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:


Harmonics

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?


Fundamental frequency

Fundamental Frequency

Click below to watch the Visual Concept.

Visual Concept


Standing waves in an air column

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 25°C).


Both ends open

Both Ends Open


Closed at one end

Closed at One End


Wind instruments

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.


P ractice problems

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.


P ractice problems1

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 25.0°C?

      • 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


P ractice problems2

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?


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