http://www.ck12.org Chapter 11. Vibrations and Sound
c. The ambulance is now stopped by the side of the road still blaring its siren at 700 Hz, and a driver is approaching
the ambulance at a velocity of 31 m/s. What frequency does the car driver hear?
Answer:The receiver is moving toward the source for an effectively higher wave speed, sovris positive.
f′=f
v+vr
v= (700 Hz)(
343 m/s+ 31 .0 m/s
343 m/s)
=763 Hzd. The car has now passed the stopped ambulance, and is moving away from the ambulance at 31 m/s. What
frequency does the driver hear?
Answer:The receiver is moving away from the sound, so effective wave speed is smaller and the velocity of the
receivervris negative.
f′=f
v+vr
v= (700 Hz)(
343 m/s+(− 31 .0 m/s)
343 m/s)
=637 Hz- Waves may interfereconstructivelyordestructively,giving rise to increases and decreases of the amplitude.
- Wave interference is responsible for the phenomenon ofbeats; where the amplitude of the sound changes
when two sounds with close frequenciesf 1 andf 2 are produced. The resulting beat frequency isfb=f 2 −f 1. - The intensity of a wave is defined as the average power produced by some source divided by the surface area
over which the energy is transmitted. The equation for the intensity isI=WA whereIrepresents intensity,W
power (the wattage) andAthe area over which the energy, in a given amount of time, has spread. - The range of human hearing is 20 Hz-20,000Hz. Frequencies higher than this are calledultrasonicfrequencies.
- The wave velocity equation isv=λfwherevis the velocity with which the wave travels;λis the wavelength
of the wave; andfis the frequency of the wave. - Many objects possess anaturalorresonantfrequency with which they vibrate. Strings and pipes (tubes) have
multiple resonant frequencies as do most musical instruments. During resonance the amplitude of vibration
of an object increases dramatically. - Both fixed strings and open pipes have resonant wavelengths ofλn=^2 nL, whereLis the length of the string
that is in resonance, andn= 1 , 2 , 3.. .. - Both strings fixed at only one end and closed pipes have resonant wavelengths ofλn=^4 nLwhereLis the
resonant length of pipe or tube, andn= 1 , 3 , 5.. .. - The Doppler effect occurs when a source of sound and/or the receiver are in motion.
f′=
v′
λ′
=f(
v+vr
v+vs)
A source moving atvschanges the wavelength. The source moving away stretches out the wavelength, giving
positivevs.
A receiver moving atvrchanges the effective wave speed. The receiver moving towards the source makes the
waves arrive faster, giving positivevr.