1. CHAPTER 14 Sound Doppler Effect A train passes by you with its whistle/horn blowing. You hear one pitch (tone) as the train is coming towards you and a different pitch after the train has passed you. Why?

2. Qualitative Explanation Sound waves travel at about 343 m/s regardless if the source is moving or not. They are not like a ball thrown at 40m/s off the front of a train which would have a ground velocity of 40m/s + train velocity. Train speed is not orders of magnitude different from the speed of sound. Movement of the train causes wave crests to “bunch up” in front of the train (higher pitch) and spread out (lower pitch) behind the train.

3. Doppler Quantitative Explanation Speed of sound: v = 343 m/s Velocity of source: v s Frequency of source: f Period of source: T Wavelength of source: Observer “A” Perspective Apparent wavelength = ’ = - distance source moved during one wave period ’ = - v s T ’ = - v s f Apparent frequency: f’ = f’ = f v ’ ( ) v v - v s ; v = f’ ’ ; ’ = - v s f

4. Speed of sound: v = 343 m/s Velocity of source: v s Frequency of source: f Period of source: T Wavelength of source: Observer “B” Perspective Apparent wavelength = ’ = + distance source moved during one wave period ’ = + v s T ’ = + v s f Apparent frequency: f’ = f’ = f v ’ ( ) v v + v s

5. Doppler Effect with Receptor (You!) Moving Moving Receptor: Apparent velocity of sound is important v’ = v + v o where v o = receptor velocity and where receptor “chasing” source v’ = v – v o where receptor avoiding source One Equation f’ = f ( ) v  v o v v s 

6. Example Problem Example Problem (Doppler Effect) The siren of a police car at rest emits a sound with a frequency of 1600Hz (Hertz). What frequency will you hear if the police car moves at 25.0 m/s a) towards you? b) away from you? Which sounds worse? a) f’ = f ( ) v  v o v v s  f = 1600 sec -1 v = 343 m/s v s = 25.0 m/s v o = 0.0 m/s f’ = (1600 -1 ) ( ) 343m/s 343 m/s – 25.0 m/s f’ = 1726 sec -1 = 1726 Hz b) f’ = (1600 sec -1 ) ( ) 343m/s 343 m/s + 25.0 m/s f’= 1491 sec -1 = 1491 Hz c) Police sirens always sound worse when they are… moving towards you!!