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PHYSICS 231 Lecture 35: interference & sound

PHYSICS 231 Lecture 35: interference & sound . Remco Zegers Question hours:Monday 9:15-10:15 Helproom. example.

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PHYSICS 231 Lecture 35: interference & sound

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  1. PHYSICS 231Lecture 35: interference & sound Remco Zegers Question hours:Monday 9:15-10:15 Helproom PHY 231

  2. example A pendulum with a length of 4 m and a swinging mass of 1 kg oscillates with an maximum angle of 10o. What is the gravitational force parallel to the string, perpendicular to the string, the total gravitational force and the centripetal force when the mass passes through the equilibrium position and when it reaches its maximum amplitude? PHY 231

  3. describing a traveling wave : wavelength distance between two maxima. While the wave has traveled one wavelength, each point on the rope has made one period of oscillation. v=x/t=/T= f On a string: v=(F/) PHY 231

  4. Interference Two traveling waves pass through each other without affecting each other. The resulting displacement is the superposition of the two individual waves. example: two pulses on a string that meet PHY 231

  5. Interference II constructive interference destructive interference PHY 231

  6.  +   = destructive interference waves ½ out of phase demo: interference Interference III + = constructive interference waves in phase PHY 231

  7. Interference IV If the two interfering waves always have the same vertical displacement at any point along the waves, but are of opposite sign: standing waves Two interfering waves can at times constructively interfere and at times destructively interfere later more!!! PHY 231

  8. Interference holds for any wave type The pulses can be sine-waves, rectangular waves or triangular waves PHY 231

  9. r1=r2 r1 r2 positive constructive interference negative constructive interference destructive interference if r2-r1=n then constructive interference occurs if r2-r1=(n+½) the destructive interference occurs Interference in spherical waves maximum of wave minimum of wave PHY 231

  10. Interference of water waves PHY 231

  11. Example two speakers separated by 0.7m produce a sound with frequency 690 Hz (from the same sound system). A person starts walking from one of the speakers perpendicular to the line connecting the speakers. After what distance does he reach the first maximum? And the first minimum? vsound=343 m/s 0.7m direction of walking person PHY 231

  12. FREE END: no inversion Reflection of waves. Frope on wall= -Fwall on rope demo: rope on wall FIXED END: pulse inversion PHY 231

  13. Connecting ropes If a pulse travels from a heavy rope to a light rope (light< heavy) the boundary is nearly free. The pulse is partially reflected (not inverted) and partially transmitted. If a pulse travels from a light rope to a heavy rope (light< heavy) the boundary is nearly fixed. The pulse is partially reflected (inverted) and partially transmitted. before before Ain Ain AR AR AT AT after |AR|<|Ain| |AT|<|Ain| after |AR|<|Ain| |AT|>|Ain| PHY 231

  14. Sound: longitudinal waves PHY 231

  15. The speed of sound Depends on the how easy the material is compressed (elastic property) and how much the material resists acceleration (inertial property) v=(elastic property/inertial property) v=(B/) B: bulk modulus : density The velocity also depends on temperature. In air: v=331(T/273 K) so v=343 m/s at room temperature PHY 231

  16. Quick question • The speed of sound in air is affected in changes in: • (more than one possible) • wavelength • frequency • temperature • amplitude • none of the above PHY 231

  17. Intensity Intensity: rate of energy flow through an area Power (P) J/s A (m2) I=P/A (J/m2s=W/m2) example: If you buy a speaker, it gives power output in Watts. However, even if you put a powerful speaker in a large room, the intensity of the sound can be small. PHY 231

  18. Intensity Faintest sound we can hear: I~1x10-12 W/m2 (1000 Hz) Loudest sound we can stand: I~1 W/m2 (1000 Hz) Factor of 1012? Loudness works logarithmic… PHY 231

  19. decibel level  =10log(I/I0) I0=10-12 W/m2 y=log10x inverse of x=10y (y=ln(x) x=ey) log(ab) =log(a)+log(b) log(a/b) =log(a)-log(b) log(an) =nlog(a) PHY 231

  20. decibels =10log(I/I0) I0=10-12 W/m2 An increase of 10 dB: intensity of the sound is multiplied by a factor of 10. 2-1=10 10=10log(I2/I0)-10log(I1/I0) 10=10log(I2/I1) 1=log(I2/I1) 10=I2/I1 I2=10I1 Next quiz! PHY 231

  21. Frequency vs intensity 1000 Hz PHY 231

  22. example A machine produces sound with a level of 80dB. How many machines can you add before exceeding 100dB? PHY 231

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