chapter 16 - sound waves speed of sound sound characteristics intensity instruments: strings and...

24
Chapter 16 - Sound Waves Speed of Sound Sound Characteristics • Intensity Instruments: Strings and Pipes 2 Dimensional Interference • Beats Doppler Effect Sonic Boom and shock waves

Upload: cathleen-walker

Post on 25-Dec-2015

221 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Chapter 16 - Sound Waves

• Speed of Sound• Sound Characteristics • Intensity• Instruments: Strings and Pipes • 2 Dimensional Interference• Beats• Doppler Effect• Sonic Boom and shock waves

Page 2: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Sound Speed Bulk modulus Bv

density

Air Sea WaterBulk Modulus 1.4(1.01 x 105) Pa 2.28 x 109 Pa

Density 1.21 kg/m3 1026 kg/m3

Speed 343 m/s 1500 m/s

Variation with Temperature:

mv 331 0.60T

s

2 3 mv 1449.05 4.57T .0521T .00023T

s

Air

Seawater

Page 3: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Pitch is frequency

Audible 20 Hz – 20000 Hz

Infrasonic < 20 Hz

Ultrasonic >20000 Hz

Middle C on the piano has a frequency of 262 Hz.What is the wavelength (in air)?

1.3 m

Page 4: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Intensity of sound• Loudness – intensity of the wave. Energy

transported by a wave per unit time across a unit area perpendicular to the energy flow.

Source Intensity (W/m2) Sound Level

Jet Plane 100 140

Pain Threshold 1 120

Siren 1x10-2 100

Busy Traffic 1x10-5 70

Conversation 3x10-6 65

Whisper 1x10-10 20

Rustle of leaves 1x10-11 10

Hearing Threshold 1x10-12 1

Page 5: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Sound Level - Decibel

0

IdB 10log

I

12

0 2

WI 1x10

m

Page 6: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Stringed instruments

nn

v nvf n=1,2,3,4,....

2L

Page 7: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Question 1

• A steel wire in a piano has a length of 0.9 m and a mass of 5.4 g. To what tension must this wire be stretched so that its fundamental vibration corresponds to middle C: i.e., the vibration possess a frequency 261.6.

Page 8: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Wind instruments – Double open ended pipes

nn

v nvf n=1,2,3,4,....

2L

Frequencies are identical to waves on a string

Page 9: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Wind instruments – Single open ended pipes

nn

v nvf n=1,3,5,7,....

4L

Only odd harmonics are present

Page 10: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Question 2 – Pepsi Bottle

• What is the fundamental frequency of a pepsi bottle 32 cm tall when you blow over it. Assume the speed of sound in air is 343 m/s.

• 5 cm of water are added to the bottle. What is the new resonant frequency.

32 cm

Page 11: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Waves on the surface of a liquid

Page 12: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Two dimensional wave reflection

i r

Page 13: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Interference in Space

When the path lengths from source to receiver differ by /2 destructive interference results.

Page 14: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Interference in Time - Beats

• Two sounds of different frequency:

1 m 1 1 m 1D x 0 D sin k 0 t D sin 2 f t

2 m 2D x 0 D sin 2 f t

• Superposition:

1 2 m 1 m 2D D D D sin 2 f t D sin 2 f t

Page 15: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

• Trig identity again:

Interference in Time - Beats

1 2 m 1 m 2D D D D sin 2 f t D sin 2 f t

1 2 1 21 2sin sin 2sin cos

2 2

1 2 1 2m

f f f fD 2D cos 2 t sin 2 t

2 2

Amplitude varies in time at a frequency equal to the difference in the two frequencies

Beat Frequency beat 1 2f f f

Page 16: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Beats

beat 1 2f f f

Page 17: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Doppler Effect

Page 18: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Doppler Effect – 4 cases

• Source moving toward receiver• Source moving away from receiver• Receiver (observer) moving towards source• Receiver (observer) moving away from source.

Page 19: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Source moving case

sv T

vT

s

s

vv 1

v v

ss

v v 1f f

vv 11vv

Towards:s

1f f

v1

v

Away:

Page 20: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Receiver (observer) moving case

O Ov v vf f 1

v

Towards:

O Ov v vf f 1

v

Away:

Page 21: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Source and receiver moving

O

O

s S

v1 v vvf f f

v v v1v

• Numerator – Receiver (observer)– Toward +– Away –

• Denominator – Source– Toward –– Away +

Page 22: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Doppler Example• Intelligence tells you that a particular piece of

machinery in the engine room of a Soviet Victor III submarine emits a frequency of 320 Hz. Your sonar operator hears the machinery but reports the frequency is 325 Hz. Assume you have slowed to a negligible speed in order to better hear the Russian.– Is the VIII coming toward you or moving away from you?

– Assuming the Victor is either moving directly toward or away from you, what is his speed in m/s?

Page 23: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Shock waves and the sonic boom

sound sound

object object

v t v 1sin

v t v m

Page 24: Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect

Sometimes you hear 2 booms