Page # Physics 103: Lecture 26 Sound. Lecture 26, Preflight 2. Lecture 26, Preflight 1. Producing a Sound Wave. Sound from a Tuning Fork

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1 Physics 103: Lecture 6 Sound Producing a Sound Wave Sound waves are longitudinal waves traveling through a medium A tuning fork can be used as an example of producing a sound wave A tuning fork will produce a pure musical note As the tines vibrate, they disturb the air near them As the tine swings to the right, it forces the air molecules near it closer together This produces a high density area in the air Area of compression Tine swings to left Area of rarefaction 5/4/06 Physics 103, Spring 004, U. Wisconsin 1 5/4/06 Physics 103, Spring 004, U. Wisconsin Sound from a Tuning Fork Categories of Sound Waves Audible waves Lay within the normal range of hearing of the human ear Normally between 0 Hz to 0,000 Hz Infrasonic waves Frequencies are below the audible range Ultrasonic waves Frequencies are above the audible range As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the fork A sinusoidal curve can be used to represent the longitudinal wave Crests correspond to compressions and troughs to rarefactions 5/4/06 Physics 103, Spring 004, U. Wisconsin 3 5/4/06 Physics 103, Spring 004, U. Wisconsin 4 Lecture 6, Preflight 1 Which of the following characterize(s) sound waves in air? 1. They are longitudinal. Their restoring force is supplied by air pressure 3. The density of the air molecules oscillates in space 4. 1 and 5. 1 and , and 3 Compression-rarefaction waves are setup by the vibrating element that produced the sound: e.g., membrane in tension on a drum, a vibrating string, 7% 9% 14% Lecture 6, Preflight Seismic waves differ from sound waves in that seismic waves 1. have a restoring force provided by the elasticity of Earth.. may propagate transversely. 3. both of the above 4. Neither of the above 15% 35% 45% 18% 5% 7% 5% 0% 10% 0% 30% 5/4/06 Physics 103, Spring 004, U. Wisconsin 5 5/4/06 Physics 103, Spring 004, U. Wisconsin 6

2 Lecture 6, Preflight 3 The speed of sound in air is a bit over 300 m/s and the speed of light in air is about 300,000,000 m/s. Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. what is the ratio of the frequency of the light wave to that of the sound wave? v = Speed of Sound elastic property inertial property 1. About 1,000,000.. About 1, About % 35% 1% 0% 0% 40% 60% v = f The speed of sound is higher in solids than in gases The molecules in a solid interact more strongly The speed is slower in liquids than in solids Liquids are more compressible Speed of waves on a string (last week s class) v = F µ Tension Mass per unit length 5/4/06 Physics 103, Spring 004, U. Wisconsin 7 5/4/06 Physics 103, Spring 004, U. Wisconsin 8 Speed of Sound in a Solid Rod The speed depends on the rod s compressibility and inertial properties v = Y Y is the Young s Modulus of the material The density of the material, Speed of Sound in a Fluid In a liquid, the speed depends on the fluid s compressibility and inertia v = B B is the Bulk Modulus of the fluid The density of the fluid: 5/4/06 Physics 103, Spring 004, U. Wisconsin 9 5/4/06 Physics 103, Spring 004, U. Wisconsin 10 Question Speed of Sound in Air The speed of sound in air is affected by changes in A. wavelength B. frequency v = B C. amplitude D. temperature E. none of the above Density varies with temperature m v = (331 ) s T 73 K Density varies with temperature - therefore, speed varies with temperature. 331 m/s is the speed of sound at 0 C T is the absolute temperature 5/4/06 Physics 103, Spring 004, U. Wisconsin 11 5/4/06 Physics 103, Spring 004, U. Wisconsin 1

3 Lecture 6, Preflight 4 A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the frequency of the sound wave inside and outside the balloon Lecture 6, Preflight 5 A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the speed of the sound wave inside and outside the balloon 1. f 1 < f 0 1. v 1 < v 0. f 1 = f 0 3. f 1 > f 0. v 1 = v 0 3. v 1 > v 0 30% f 0 f 1 8% 4% 31% 8% 41% V 0 =343m/s V 1 =965m/s Frequency of wave does not change - the wave is generated due to a driven oscillator Table 14.1: Speed of sound depends on 5/4/06 and keeps its frequency. the properties of the medium. Physics 103, Spring 004, U. Wisconsin 13 5/4/06 Physics 103, Spring 004, U. Wisconsin 14 Lecture 6, Preflight 6 A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the wavelength of the sound wave inside and outside the balloon 1. 1 < 0. 1 = > 0 7% 45% 0 1 Intensity of Sound Waves The intensity of a wave is the rate at which the energy flows through a unit area, A, oriented perpendicular to the direction of travel of the wave E P I = = A t A P is the power, the rate of energy transfer Units are W/m 7% Since v increases and f remains the same, = v/f, also increases. 5/4/06 Physics 103, Spring 004, U. Wisconsin 15 5/4/06 Physics 103, Spring 004, U. Wisconsin 16 Various Intensities of Sound Threshold of hearing Faintest sound most humans can hear About 1 x 10-1 W/m Threshold of pain Loudest sound most humans can tolerate About 1 W/m The ear is a very sensitive detector of sound waves Intensity Level of Sound Waves The sensation of loudness is logarithmic in the human hear The intensity level or the decibel level of the sound, : I = 10 log I o I o is the threshold of hearing: I 0 = 1.0 x 10-1 W/m Threshold of hearing is 0 db Threshold of pain is 10 db Jet airplanes are about 150 db 5/4/06 Physics 103, Spring 004, U. Wisconsin 17 5/4/06 Physics 103, Spring 004, U. Wisconsin 18

4 Spherical Waves A spherical wave propagates radially outward from the oscillating sphere The energy propagates equally in all directions The intensity is P I = 4r Intensity of a Point Source Since the intensity varies as 1/r, this is an inverse square relationship The average power is the same through any spherical surface centered on the source To compare intensities at two locations, the inverse square relationship can be used I I 1 r = r 1 5/4/06 Physics 103, Spring 004, U. Wisconsin 19 5/4/06 Physics 103, Spring 004, U. Wisconsin 0 Lecture 6, Preflight 7 Suppose you are standing a distance D away from a speaker that is radiating sound in a spherically uniform way. You walk away from the speaker until the loudness of sound is reduced from 0 db to 10 db. About how far from the speaker are you now (neglecting any reflections from the ground)? 1. 10D.. 4 D. 3. 3D. 4. D. Because of the uniform sphere of sound radiation, intensity drops off like 1/r. If you are 3 times as far away, the intensity of the sound will be reduced by a factor of 9. Representations of Waves Wave fronts are the concentric arcs The distance between successive wave fronts is the wavelength Rays are the radial lines pointing out from the source and perpendicular to the wave fronts 11% 14% 18% 57% Round this off to 10. Reducing the intensity I by a factor of 10 will reduce log(i/i 0 ) by 1, and since =10log(I/I 0 ), it will reduce by 10. 0% 0% 40% 60% 5/4/06 Physics 103, Spring 004, U. Wisconsin 1 5/4/06 Physics 103, Spring 004, U. Wisconsin Far away from the source, the wave fronts are nearly parallel planes The rays are nearly parallel lines A small segment of the wave front is approximately a plane wave Plane Wave Doppler Effect A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. When the source and the observer are moving toward each other, the observer hears a higher frequency When the source and the observer are moving away from each other, the observer hears a lower frequency Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves 5/4/06 Physics 103, Spring 004, U. Wisconsin 3 5/4/06 Physics 103, Spring 004, U. Wisconsin 4

5 An observer is moving toward a stationary source Due to his movement, the observer detects an additional number of wave fronts The frequency heard is increased Doppler Effect, Case 1 An observer is moving away from a stationary source The observer detects fewer wave fronts per second The frequency appears lower Doppler Effect, Case Fig 14.8, p. 435 Slide 1 Fig 14.9, p. 436 Slide 13 5/4/06 Physics 103, Spring 004, U. Wisconsin 5 5/4/06 Physics 103, Spring 004, U. Wisconsin 6 Doppler Effect, Summary of Observer Moving The apparent frequency, ƒ, depends on the actual frequency of the sound and the speeds v + vo ƒ' = ƒ v v o is positive if the observer is moving toward the source and negative if the observer is moving away from the source Doppler Effect, Source in Motion As the source moves toward the observer (A), the wavelength appears shorter and the frequency increases As the source moves away from the observer (B), the wavelength appears longer and the frequency appears to be lower 5/4/06 Physics 103, Spring 004, U. Wisconsin 7 5/4/06 Physics 103, Spring 004, U. Wisconsin 8 Doppler Effect, Source Moving Doppler Effect, both moving Both the source and the observer could be moving Use the v s when the source is moving toward the observer and +v s when the source is moving away from the observer v ƒ' = ƒ v v s v + v ƒ' = ƒ v v Use positive values of v o and v s if the motion is toward Frequency appears higher Use negative values of v o and v s if the motion is away Frequency appears lower o s 5/4/06 Physics 103, Spring 004, U. Wisconsin 9 5/4/06 Physics 103, Spring 004, U. Wisconsin 30

6 Lecture 6, Preflight 8 Consider the following two cases: A: You are driving along the highway at 65 mph, and behind you a police car, also traveling at 65 mph, has its siren turned on. B: You and the police car have both pulled over to the side of the road, but the siren is still turned on. In which case does the frequency of the siren seem higher to you? Case A Case B The siren will sound the same in both cases Lecture 6, Preflight 9 You are at rest on a platform at a railroad station. A train approaches the platform blowing its whistle. As the train passes you, the pitch of the whistle 1. increases.. decreases. 3. stays the same. 4. depends on the amplitude of the sound. 3% 31% 43% It is the relative speed that causes Doppler effect. In both cases the relative speed is zero. % 0% 46% 7% 5/4/06 Physics 103, Spring 004, U. Wisconsin 31 5/4/06 Physics 103, Spring 004, U. Wisconsin 3