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Presentation Transcript

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?

- What is the same about the sound?

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

- 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 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

- 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?

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).

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.

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.

- What is the wavelength of the first harmonic or the fundamental wavelength?

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

- What is the wavelength of the first harmonic or the fundamental wavelength?

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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