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1、Sound Beats,Superposition leads to beats variation in loudness,Resonance,Occurs in fixed media length L Depends on boundary conditions Occurs only for certain frequencies for which an integral number of or wavelengths fit in medium length L Affected by propagation speed in medium,Boundary Conditions
2、,Ends of medium are either a node or antinode Determined by the configuration of the system Stringed instruments both ends are nodes Woodwinds, brass, organs one end is always an antinode, the other end can be either,Procedure,Identify physical situation (string or air column) Identify boundary cond
3、itions (nodes or antinodes) If the same use wavelengths If different use wavelengths Sketch waveforms determine how many or fit in length L For each allowed n, solve for n Determine propagation speed v Use v = f to find fn,Harmonic Series of Standing Waves on a Vibrating String,Both ends are nodes (
4、N) use s Sketch Solve for n If v not known use Solve for fn,Harmonic Series of a Pipe Open at Both Ends,Both ends are antinodes (A) use wavelengths Sketch Solve for n If v not known use Solve for fn,Harmonic Series of a Pipe Open at One End,One end A, other end N use wavelengths Sketch Solve for n I
5、f v not known use Solve for fn,Harmonics for Same Ends,Note that when ends are both nodes or both antinodes, n = 1, 2, 3, 4, f2 = 2f1 2nd harmonic or 1st overtone f3 = 3f1 3rd harmonic or 2nd overtone f4 = 4f1 4th harmonic or 3rd overtone f5 = 5f1 5th harmonic or 4th overtone And so on fn = nf1,Harm
6、onics for Different Ends,Note that when one end is N and the other is A, n = 1, 3, 5, 7, f3 = 3f1 3rd harmonic or 2nd overtone f5 = 5f1 5th harmonic or 4th overtone f7 = 7f1 7th harmonic or 6th overtone f9 = 9f1 9th harmonic or 8th overtone And so on fn = nf1 only odd harmonics are allowed,Propagati
7、on Speed,In a string v depends on the tension T and linear mass density lin In an air column v depends on temperature T,Sound Levels,Decibel or dB scale,I0 is the threshold of hearing Threshold of pain is 120 dB,The Doppler Effect,An observer of the wave crests behind or away from the direction of m
8、otion would identify a lower frequency due to a greater travel distance from the vibration source. This apparent change in frequency is called the DOPPLER EFFECT after Christian Doppler (1803 1853) The greater the speed, the greater the Doppler effect The police and weather reporters use the Doppler
9、 effect of radar waves to measure the speeds of cars or water in clouds.,The Doppler Effect,Vibrating in a stationary position produces waves in concentric circles. (because the wave speed is the same in all directions),Vibrating while moving at a speed less than the wave speed produces nonconcentri
10、c circles. The wave crests in the direction of motion occur more often (have a higher frequency) due to a shorter travel distance.,Doppler Effect,If source (s) is moving, detected frequency (fd) changes If detector (d) is moving, detected frequency changes,Top sign when moving away from Bottom sign
11、when moving towards,Astronomy and the Doppler Shift,Astronomers can measure the Doppler Shift of a moving object. The radio wave has a known frequency for stationary objects. If target is moving away, waves in the signal will be stretched, and will have a lower frequency. The Doppler shift is called
12、 “Red shift” if v 0 (moving away) since the wavelength is getting longer and the frequency shorter “Blue Shift” if v 0 (moving closer) since the wavelength is getting shorter and the frequency higher (recall that blue light is higher in frequency than red),TWO CLIPS ON THE DOPPLER EFFECT,Bow Waves,W
13、hen the vibration source is moving at the same speed as the wave front, a bow wave is produced. In aircraft this is called the “sound barrier”. It is not a real barrier, but is where the wave crests build up on each other at the speed of sound. Speedboats and supersonic aircraft travel in front of their bow waves.,Shock Waves,Shock waves produced by supersonic aircraft are the 3-dimensional version of the V-shaped bow wave produced by boats. On the ground this is noted as a sonic boom.,SIMULATIONS FOR DOPPLER EFFECT AND BOW WAVES,http:/www.astro.ubc.ca/scharein/a311/Sim/doppler/Doppler.html,
