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  After giving an intense performance, a confused and disoriented flautist has wandered onto the motorway! They are playing a constant 300 Hz tone on their flute and are essentially stationary. If you are driving along the motorway at 100 km h−1 (27.8 m s−1 ), what is the frequency you hear from the flautist’s instrument before you pass them? (cair= 343 m s−1 .)



Answer :

olemakpadu
This is a Doppler effect. Generally, if you move to a frequency source, you would detect an increase in frequency and when you move away from a source you would detect a decrease.

For this question, before you pass them, you are actually approaching them, so you would hear a higher frequency than the constant 300 Hz they are playing at.

Using the condensed formula:

 f '   =   ((v + vd)/(v + vs)) * f

Where:  vd = Velocity of the detector.
              vs = Velocity of the frequency source.
              v   =  Velocity of sound in air.
              f '  =  Apparent frequency.
              f    =  Frequency of source.

v = 343 m/s,  vd = detector = 27.8 m/s,  vs = velocity of the source =0. (the flautists are not moving).
f = 300 Hz. 

There would be an overall increase in frequency, so we maintain a plus at the numerator and a minus at the denominator.

 f '   =   ((v + vd)/(v - vs)) * f

f '   =   ((343+ 27.8)/(343 - 0)) * 300
      =   (370.8/343)* 300 =  324.3

Therefore frequency before passing them = 324.3 Hz.

Cheers.

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