12.2 SoundComplex Sound WavesBeatsDoppler Effect.Complex waves• In general sound waves are a combination of different frequencies. • The different frequencies can be determined by mathematical procedure called a Fourier Transform. TimedisplacementFrequencyrelativeamplitudeComplex waves consist of different frequencycomponents , i.e. harmonics.Frequency dependence of HearingBeatsSuperposition of two waves with different frequencies produce oscillation in amplitude. Due to constructive and destructive interference.Tbb21b1fffT==−Beat FrequencyTuning musical instrumentsThe beat frequency for two musical instruments is zero when the two are in tune. (have the same frequency)2Doppler EffectDoppler effect- the shift in frequency of a wave where the source and observer are moving relative to one another.Two different cases:Observer moving – source stationarySource moving- observer stationary.Observer moving toward a Stationary source (Relative Velocity Increases)ooossvvvvffv++==λWhen observer is moving toward sourcethe frequency increases.The wavelength in the media is unchanged but the relative velocity (vo+ v ) between the observer and the wave is increasedObserver moving away from a stationary source (Relative velocity decreases) oosoosvvfvvffv−=λ−=When observer is moving away from the sourcethe frequency decreases. (use – vo)the relative velocity between the observer and the wave is decreasedthenVovochanges signSource moving toward a stationary observer(wavelength in the medium decreases)•When the source is moving the wavelength of the wave in the media is changed•when the source approaches an observer•Wavelength decreases and frequency increasesosss sssvvfvT vT vT==λ− −ossvffvv=−foincreases whensource moves towardobserver.vSource Moving Toward observer A•Wavelength decreasesosss sssvvfvT vT vT==λ− −ossvffvv=−Moving Source ObserversvTλ=λ −Frequency increasesSource Moving Away from observer B•Wavelength increasesosss sssvvfvT vT vT==λ+ +ossvffvv=+Moving SourceObserversvTλ=λ +Frequency decreasesλ3General caseoossvvffvv⎛⎞+=⎜⎟−⎝⎠vsvovvopositive when observer is moving toward sourcevonegative when observer is moving away from sourcevspositive when source is moving toward observervsnegative when source is moving away from observer.sourceobserverExampleA fire truck is approaching an observer with a speed of 30 m/s. The siren has a frequency of 700 Hz. What frequency does the observer hear as the truck approaches? What frequency is heard after the truck passes. speed of sound 340 m/sApproaching sourceoos sssvvvff fvv vv⎛⎞⎛⎞+==⎜⎟⎜⎟−−⎝⎠⎝⎠()340700 700 1.09 763Hz340 30⎛⎞===⎜⎟−⎝⎠Departing sourceoos sssvvvff fvv vv⎛⎞⎛⎞+==⎜⎟⎜⎟−−⎝⎠⎝⎠()340700 700 0.92 643Hz340 30⎛⎞===⎜⎟+⎝⎠vsis negativevspositiveDoppler shift of Electromagnetic waves• Electromagnetic waves are also shifted by the Doppler effect.• Since EM waves travel in a vacuum the equations governing the shift are different.• The same shift is observed for moving source or moving observer.• For motion with speeds less than the speed of light the relation is the same as for the approximate shift for sound waves when u<<v.suff(1 )c=±U = relative velocities of source and observe.Positive sign when approachingNegative sign when moving away.Doppler Radarfo1fo2fDoppler radar is used to determine the speed of a car.The beat frequency between the Doppler shifted frequency and the initial frequency is measured to determine the speed of the