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Understanding Sound Waves Interactions: Frequency, Intensity, and Doppler Effect

Explore the behavior of sound waves in different mediums and scenarios, including frequency changes inside a balloon, intensity calculations, and Doppler effects. Learn about destructive and constructive interference.

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Understanding Sound Waves Interactions: Frequency, Intensity, and Doppler Effect

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  1. Sound

  2. Speed of Sound • Recall for pulse on string: v = sqrt(F / m) • For fluids: v = sqrt(B/r) 05

  3. V1=965m/s V0=343m/s Velocity Question A sound wave having frequency f0, speed v0 and wavelength l0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f1, its speed is v1, and its wavelength is l1Compare the speed of the sound wave inside and outside the balloon 1. v1 < v0 2. v1 = v0 3. v1 > v0 10

  4. f0 f1 Frequency Question A sound wave having frequency f0, speed v0 and wavelength l0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f1, its speed is v1, and its wavelength is l1Compare the frequency of the sound wave inside and outside the balloon 1. f1 < f0 2. f1 = f0 3. f1 > f0 Time between wave peaks does not change! 13

  5. l1 l0  = v / f Wavelength Question A sound wave having frequency f0, speed v0 and wavelength l0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f1, its speed is v1, and its wavelength is l1Compare the wavelength of the sound wave inside and outside the balloon 1. l1 < l0 2. l1 = l0 3. l1 > l0 15

  6. Intensity and Loudness • Intensity is the power per unit area. • I = P / A • Units: Watts/m2 • For Sound Waves • I = p02 / (2 r v)(po is the pressure amplitude) • Proportional to p02(note: Energy goes as A2) • Loudness(Decibels) • Loudness perception is logarithmic • Threshold for hearing I0 = 10-12 W/m2 • b = (10 dB) log10 ( I / I0) • b2 – b1 = (10 dB) log10(I2/I1) 18

  7. Log10 Review • Log10(1) = • Log10(10) = • Log 10(100) = • Log10(1,000) = • Log10(10,000,000,000) = 19

  8. Decibels Question • If 1 person can shout with loudness 50 dB. How loud will it be when 100 people shout? 1) 52 dB 2) 70 dB 3) 150 dB 22

  9. Speaker radiating power P I1 = P/(4pD12) D1 I2 = P/(4pD22) D2 Intensity Question • Recall Intensity = P/A. If you are standing 6 meters from a speaker, and you walk towards it until you are 3 meters away, by what factor has the intensity of the sound increased? 1) 2 2) 4 3) 8 Area goes as d2 so if you are ½ the distance the intensity will increase by a factor of 4 27

  10. Standing Waves in Pipes Open at one end: Pressure AntiNode at closed end :l = 4 L / n n odd Open at both ends: Pressure Node at end l = 2 L / n n=1,2,3.. 29

  11. Example: Organ Pipe A 0.9 m organ pipe (open at both ends) is measured to have it’s first harmonic at a frequency of 382 Hz. What is the speed of sound in the pipe? 32

  12. Dopper shift • As a police car passes you with its siren on, the frequency of the sound you hear from its siren 1) Increases 2) Decreases 3) Same Doppler Example Audio Doppler Example Visual 36

  13. Doppler Effect moving source vs • When source is coming toward you (vs > 0) • Distance between waves decreases • Frequency increases • When source is going away from you (vs < 0) • Distance between waves increases • Frequency decreases • fo = fs / (1- vs/v) 38

  14. Doppler Effect moving observer (vo) • When moving toward source (vo < 0) • Time between waves peaks decreases • Frequency increases • When away from source (vo > 0) • Time between waves peaks increases • Frequency decreases • fo = fs (1- vo/v) Combine:fo = fs (1-vo/v) / (1-vs/v) 40

  15. Example: police car A police car is approaching you from behind so you pull over to the side of the road and stop. If the police car is moving at 25m/s and the siren is emitting a sound with frequency 200Hz. What frequency do you hear? Speed of sound = 330m/s 44

  16. Example: police car If the police car is moving at 25m/s and the siren is emitting a sound with frequency 200Hz. After the police car passes you what frequency do you hear? Speed of sound = 330m/s 44

  17. Superposition & Interference • Consider two harmonic waves A and B meeting at x=0. • Same amplitudes, but 2 = 1.15 x 1. • The displacement versus time for each is shown below: A(1t) B(2t) What does C(t) =A(t)+B(t) look like?? 46

  18. DESTRUCTIVEINTERFERENCE CONSTRUCTIVEINTERFERENCE Superposition & Interference • Consider two harmonic waves A and B meeting at x=0. • Same amplitudes, but 2 = 1.15 x 1. • The displacement versus time for each is shown below: A(1t) B(2t) C(t) =A(t)+B(t) 47

  19. Summary • Speed of sound v = sqrt(B/r) • Intensity B = (10 dB) log10 ( I / I0) • Standing Waves • fn = n v/(2L) Open at both ends n=1,2,3… • fn = n v/(4L) Open at one end n=1,3,5… • Doppler Effect fo = fs (v-vo) / (v-vs) • Beats 50

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