SoundSound13-313-3

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 A violin, a trumpet, and a clarinet all play the same note, a concert A. play the same note, a concert A. However, they all sound different.However, they all sound different.• What is the same about the sound? What is the same about the sound?

• Are the frequencies produced the same?Are the frequencies produced the same?• Are the wave patterns the same?Are the wave patterns the same?

• Why do the instruments sound Why do the instruments sound different?different?

Standing WavesStanding Waves

Standing waves are produced when Standing waves are produced when two identical waves travel in two identical waves travel in opposite directions and interfere.opposite directions and interfere. Interference alternates between Interference alternates between

constructive and destructive.constructive and destructive. Nodes are points where interference Nodes are points where interference

is always destructive.is always destructive. Antinodes are points between the Antinodes are points between the

nodes with maximum displacement.nodes with maximum displacement.

Standing Waves on a Standing Waves on a StringString

There is a node at each end because There is a node at each end because the string is fixed at the ends.the string is fixed at the ends.

The diagram shows three possible The diagram shows three possible standing wave patterns.standing wave patterns.

Standing waves are produced by Standing waves are produced by interference as waves travel in interference as waves travel in opposite directions after plucking or opposite directions after plucking or bowing the string.bowing the string.

The lowest frequency (one loop) is The lowest frequency (one loop) is called the fundamental frequency called the fundamental frequency ((ff11).).

Standing Waves on a Standing Waves on a StringString

To the left is a To the left is a snapshot of a single snapshot of a single loop standing wave loop standing wave on a string of on a string of length, length, LL..

What is the What is the wavelength for this wavelength for this wave?wave? Answer: Answer: = 2 = 2LL

What is the What is the frequency?frequency? Answer:Answer:

1 2

v vf

L

Harmonics Harmonics

nn is the number of loops or harmonic number. is the number of loops or harmonic number. vv is the speed of the wave on the string. is the speed of the wave on the string.

Depends on tension and density of the stringDepends on tension and density of the string LL is the length of the vibrating portion of the string. is the length of the vibrating portion of the string. How could you change the frequency (pitch) of a How could you change the frequency (pitch) of a

string?string?

Click below to watch the Visual Concept.

Visual Concept

Fundamental Frequency Fundamental Frequency

Wind instruments also Wind instruments also use standing waves.use standing waves. Flutes, trumpets, pipe Flutes, trumpets, pipe

organs, trombones, etc.organs, trombones, etc. Some instruments have Some instruments have

pipes open at both ends pipes open at both ends while others have one while others have one end closed.end closed. Air is free to move at open Air is free to move at open

ends so antinodes occur.ends so antinodes occur. Closed ends are nodes.Closed ends are nodes.

The velocity of the wave The velocity of the wave is now the velocity of is now the velocity of sound in air (346 m/s at sound in air (346 m/s at 25°C).25°C).

Standing Waves in an Air Standing Waves in an Air ColumnColumn

Both Ends OpenBoth Ends Open

Closed at One EndClosed at One End

Wind InstrumentsWind Instruments

Wind instruments are not as simple Wind instruments are not as simple as organ pipes.as organ pipes. The shape is not always cylindrical.The shape is not always cylindrical. The holes change the wave patterns as The holes change the wave patterns as

well.well. The size of the “pipe” varies along the The size of the “pipe” varies along the

length.length.

PPracticeractice Problems Problems

One string on a toy guitar is 34.5 cm long.One string on a toy guitar is 34.5 cm long. What is the wavelength of the first harmonic What is the wavelength of the first harmonic

or the fundamental wavelength?or the fundamental wavelength? Answer: 69.0 cm or 0.690 mAnswer: 69.0 cm or 0.690 m

The string is plucked and the speed of the The string is plucked and the speed of the waves on the string is 410 m/s. What are the waves on the string is 410 m/s. What are the frequencies of the first three harmonics?frequencies of the first three harmonics? 590 Hz, 1200 Hz, 1800 Hz590 Hz, 1200 Hz, 1800 Hz Note: The use of significant figures causes the Note: The use of significant figures causes the

multiples of 590 to be 1200 and 1800 because only multiples of 590 to be 1200 and 1800 because only two significant figures are present in the answer.two significant figures are present in the answer.

PPractice Problemsractice Problems An organ pipe open at both ends is 34.5 An organ pipe open at both ends is 34.5

cm long.cm long. What is the wavelength of the first harmonic What is the wavelength of the first harmonic

or the fundamental wavelength?or the fundamental wavelength? Answer: 69.0 cm or 0.690 mAnswer: 69.0 cm or 0.690 m

What are the frequencies of the first three What are the frequencies of the first three harmonics if the air temperature is 25.0°C?harmonics if the air temperature is 25.0°C?

Answers: 501 Hz, 1000 Hz, 1500 HzAnswers: 501 Hz, 1000 Hz, 1500 Hz Answer the same questions if the pipe is Answer the same questions if the pipe is

closed at one end.closed at one end. Answers: 251 Hz, 753 Hz, 1250 HzAnswers: 251 Hz, 753 Hz, 1250 Hz

PPractice Problemsractice Problems

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