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UNIT 7Waves, Vibrations, and

Sound

Thursday February 2nd

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WAVES, VIBRATIONS, AND SOUND

TODAY’S AGENDA

More on HarmonicsProblem Quiz #2

UPCOMING…

Fri: Inertial Balance Lab Mon: Problem Quiz #3 Tue: Speed of Sound Lab

Thursday, February 2

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(1) the long pipe

(2) the short pipe

(3) both have the same frequency

(4) depends on the speed of sound in the pipe

You have a long pipe

and a short pipe.

Which one has the

higher frequency?

ConcepTest 14.12a Pied Piper I

A shorter pipe means that the standing wave in

the pipe would have a shorter wavelength. Since

the wave speed remains the same, the frequency

has to be higher in the short pipe.

(1) the long pipe

(2) the short pipe

(3) both have the same frequency

(4) depends on the speed of sound in the pipe

You have a long pipe

and a short pipe.

Which one has the

higher frequency?

ConcepTest 14.12a Pied Piper I

A wood whistle has a variable length. You just heard the tone from the whistle at maximum length. If the air column is made shorter by moving the end stop, what happens to the frequency?

1) frequency will increase

2) frequency will not change

3) frequency will decrease

ConcepTest 14.12b Pied Piper II

A wood whistle has a variable length. You just heard the tone from the whistle at maximum length. If the air column is made shorter by moving the end stop, what happens to the frequency?

1) frequency will increase

2) frequency will not change

3) frequency will decrease

A shorter pipe means that the standing wave in the pipe would have a shorter wavelength. Since the wave speed remains the same, and since we know that v = f l, then we see that the frequency has to increase when the pipe is made shorter.

ConcepTest 14.12b Pied Piper II

If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change?

1) frequency will increase

2) frequency will not change

3) frequency will decrease

ConcepTest 14.12c Pied Piper III

If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change?

1) frequency will increase

2) frequency will not change

3) frequency will decrease

By drinking some of the soda, you have effectively increased the length of the air column in the bottle. A longer pipe means that the standing wave in the bottle would have a longer wavelength. Since the wave speed remains the same, and since we know that v = f l, then we see that the frequency has to be lower.

ConcepTest 14.12c Pied Piper III

Follow-up: Why doesn’t the wave speed change?

Chapter 12

Sound

Units of Chapter 12

• Characteristics of Sound

• Intensity of Sound: Decibels

• The Ear and Its Response; Loudness

• Sources of Sound: Vibrating Strings and Air Columns

• Quality of Sound, and Noise; Superposition

• Interference of Sound Waves; Beats

• Doppler Effect

Units of Chapter 12

• Shock Waves and the Sonic Boom

• Applications: Sonar, Ultrasound, and Medical Imaging

Standing Waves; String

The frequencies of the standing waves on a particular string are called resonant frequencies.

They are also referred to as the fundamental and harmonics.

Standing Waves; Strings

The wavelengths and frequencies of standing waves are:

Standing Waves in Air Columns

• If one end of the air column is closed, a node must exist at this end since the movement of the air is restricted

• If the end is open, the elements of the air have complete freedom of movement and an antinode exists

Tube Open at Both Ends

Resonance in Air Column Open at Both Ends

• In a pipe open at both ends, the natural frequency of vibration forms a series whose harmonics are equal to integral multiples of the fundamental frequency

1ƒ ƒ 1, 2, 3,2n

vn n n

L

Tube Closed at One End

Resonance in an Air Column Closed at One End

• The closed end must be a node• The open end is an antinode

• There are no even multiples of the fundamental harmonic

1ƒ 1, 3, 5,4n

vf n n n

L

Beats

• Beats are alternations in loudness, due to interference

• Waves have slightly different frequencies and the time between constructive and destructive interference alternates

• The beat frequency equals the difference in frequency between the two sources:

2 1ƒ ƒ ƒb

Quality of Sound – Tuning Fork

• Tuning fork produces only the fundamental frequency

Quality of Sound – Flute

• The same note played on a flute sounds differently

• The second harmonic is very strong

• The fourth harmonic is close in strength to the first

Quality of Sound – Clarinet

• The fifth harmonic is very strong

• The first and fourth harmonics are very similar, with the third being close to them

Timbre

• In music, the characteristic sound of any instrument is referred to as the quality of sound, or the timbre, of the sound

• The quality depends on the mixture of harmonics in the sound

Pitch

• Pitch is related mainly, although not completely, to the frequency of the sound

• Pitch is not a physical property of the sound• Frequency is the stimulus and pitch is the

response– It is a psychological reaction that allows humans to

place the sound on a scale

Doppler Effect

As can be seen in the previous image, a source moving toward an observer has a higher frequency and shorter wavelength; the opposite is true when a source is moving away from an observer.

Shock Waves and the Sonic Boom

If a source is moving faster than the wave speed in a medium, waves cannot keep up and a shock wave is formed.

The angle of the cone is: (12-5)

Shock Waves and the Sonic Boom

Shock waves are analogous to the bow waves produced by a boat going faster than the wave speed in water.

Shock Waves and the Sonic Boom

Aircraft exceeding the speed of sound in air will produce two sonic booms, one from the front and one from the tail.

Applications: Sonar, Ultrasound, and Medical Imaging

Sonar is used to locate objects underwater by measuring the time it takes a sound pulse to reflect back to the receiver.

Similar techniques can be used to learn about the internal structure of the Earth.

Sonar usually uses ultrasound waves, as the shorter wavelengths are less likely to be diffracted by obstacles.

Ultrasound is also used for medical imaging. Repeated traces are made as the transducer is moved, and a complete picture is built.

Applications: Sonar, Ultrasound, and Medical Imaging

Ordinary ultrasound gives a good picture; high-resolution ultrasound is excellent.

Applications: Sonar, Ultrasound, and Medical Imaging

Summary of Chapter 12

• Sound is a longitudinal wave in a medium.

• The pitch of the sound depends on the frequency.

• The loudness of the sound depends on the intensity and also on the sensitivity of the ear.

• The strings on stringed instruments produce a fundamental tone whose wavelength is twice the length of the string; there are also various harmonics present.

Summary of Chapter 12

• Wind instruments have a vibrating column of air when played. If the tube is open, the fundamental is twice its length; if it is closed the fundamental is four times the tube length.

• Sound waves exhibit interference; if two sounds are at slightly different frequencies they produce beats.

• The Doppler effect is the shift in frequency of a sound due to motion of the source or the observer.

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