Analytical Physics 1B Lecture 7: Sound

Transcription

1 Analytical Physics 1B Lecture 7: Sound Sang-Wook Cheong Friday, March 2nd, 2018

2 Sound Waves Longitudinal waves in a medium (air, solids, liquids, etc.) Human ear is sensitive to frequencies between 20 and 20,000 Hz Think about sound as a variation of pressure as a function of position and time 2

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4 Sound Waves Let p(x,t) be how much the pressure differs from the normal atmospheric pressure The maximum difference in pressure pmax (a.k.a. the pressure amplitude) can be related to properties of the wave k is the wavenumber A is the displacement amplitude B is the bulk modulus (this is like a 3D spring constant) Compressibility: how much a material s volume changes when put under a fixed pressure. Bulk modulus is the inverse of compressibility. 4

5 Moderate loudness sound of 1000 Hz: P max =3x10-2 Pa, the speed of sound is 344 m/s and bulk modulus: 1.42x10 5 Pa k=2 / =2 f/v=(2 rad)(1000 Hz)/344 m/s=18.3 rad A=P max /Bk=3x10-2 Pa/(1.42x10 5 Pa)(18.3 rad/m)=1.2x10-8 m=120 A o 1 m=10-6 m 1 nm=10-9 m o 1 A=10-10 m Humane hair thickness: 20 m Si-Si distance in silicon: 4 A o 5

6 Sound Intensity Intensity is like loudness However, loudness is perceptual and depends on the frequency Intensity is the power (power=energy per unit time) per unit area Intensity decreases with distance proportional to 1/r 2 (like gravity) 6

7 Sound Intensity Measured in decibels 7

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9 A 10-min exposure to 120-dB sound will temporarily shift your threshold of hearing at 1000 Hz from 0 db up to 28 db. Ten years of exposure to 92-dB sound will cause a permanent shift to 28 db.

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11 Open and Closed Pipes Characteristic frequencies of a pipe depend on its length and whether it is open or closed (As well as the speed of sound in air) 11

12 Minor Major

13 Interference Sounds waves interfere in the same way that mechanical waves interfere Suppose you have two identical waves being transmitted by two different speakers Constructive interference occurs when the distance travelled by the two differs by an integer # of wavelengths 0, λ, 2λ, 3λ, Destructive interference occurs when the distance travelled by the two differs by a half-integer # of wavelengths λ/2, 3λ/2, 5λ/2, 13

14 Noise Cancelling Headphones

15 2D Interference Two identical point sources are generating waves with the same frequency and amplitude. The two sources are in phase with each other, so the two sources generate wave crests at the same instant. The distance between the two sources is equal to two wavelengths, or 2λ. List all points where the waves from the two sources constructively interfere. A. All are constructive B. D & A C. C & F D. D & E E. A, B, D, & E 15

16 Beats If two sound waves are played with the same amplitude and nearly the same frequency, you hear a beat 16

17 Guitar Beat I A guitar string is strummed near a tuning fork that has a frequency of 512 Hz. Initially, the guitar and tuning fork together create a sound wave with a beat frequency of 5 Hz. The tension in the guitar string is then increased, after which the guitar and tuning fork together create a sound wave with a beat frequency of 4 Hz. Before the tension in the guitar string is increased, is the frequency of the guitar string: A. It is impossible to determine B. Greater than 512 Hz C. Less than 512 Hz D. Equal to 512 Hz 17

18 Guitar Beat II A guitar string is strummed near a tuning fork that has a frequency of 512 Hz. Initially, the guitar and tuning fork together create a sound wave with a beat frequency of 5 Hz. The tension in the guitar string is then increased, after which the guitar and tuning fork together create a sound wave with a beat frequency of 4 Hz. After the tension in the guitar string is increased, is the frequency of the guitar string: A. It is impossible to determine B. Greater than 512 Hz C. Less than 512 Hz D. Equal to 512 Hz 18

19 Doppler Effect Consider the case when an observer is moving towards a stationary source The frequency of the listener is 19

20 Doppler Effect When the source is moving, the situation is more complicated The wavelengths behind the direction of motion are stretched out The wavelengths in front of the direction of motion are compressed 20

21 Doppler Effect The wavelength in front of the source is The wavelength behind the source is 21

22 Doppler Effect The frequency heard by the listener is Note that the velocities are signed (that is there is an implied direction) 22

23 Police Car A police car with a 600 Hz siren is traveling along the same street as a motorcycle. The velocities of the two vehicles and the distance between them are given in each figure. Rank the frequency of the siren as measured by the motorcycle rider. A. B > A > D > C B. C > D > A > B C. D > B > A > C D. B = C > A = D E. All hear the same frequency. 23

24 Approaching Train A train approaches a station at a constant speed, sounding its whistle continuously. Three students are discussing what an observer standing at a station would hear as the train is approaching. With which, if any, of these students do you agree? Anish: "The train is not accelerating or decelerating. I think the observer will hear a constant pitch that matches the pitch of the whistle. Brooke: "Even if it isn't accelerating, the observer will hear a higher pitch than the whistle actually emits since the train is moving toward the observer. I agree that the observer will hear a constant pitch. " Cruz: "I agree with Brooke that the observer will hear a higher pitch, but I think the observer will also hear the frequency increase constantly as the train gets closer and closer." A.Anish B.Brooke C.Cruz D.None of them 24