Activity 1 (-20-25 min): This is pg. 945 # 44]. A sound with frequency f, is pro

Question

Activity 1 (-20-25 min): This is pg. 945 # 44]. A sound with frequency f, is produced by a source travelling along a line with speed v. . If an observer is travelling with speed Vo along the same line from the opposite direction toward the source, then heard by the observer is the frequency of the sound C-v where c is the speed of sound, about 332 m/s. This is the Doppler Effect. Suppose that, at a particular moment, you are in a train travelling at 34 m/s and accelerating at 1.2 m/s2. A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.4 m/s, and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear and how fast is it changing?

Explanation / Answer

at the givne instant

c = 332 , vs = 40 m/s , vo = 34 m/s , fs = 460

fo = (332+34)/ (332-40) * 460 = 576.58 Hz , percived frequency

fo*(c-vs) = fs (c+vo)

differentiate it wrt t

-fo dvs/dt +(c-vs) dfo/dt = fs dvo/dt   , fs is const.

dvs/dt = as = 1.4 m/s/s , accelertion of source

dvo/dt = ao = 1.2 m/s/s , acceleration of obeserver

rate of change

dfo/dt = 1/(c-vs) * (fs ao + fo as )

           = 1/(332-40) * (460*1.2 + 576.58 *1.4)

            = 4.65 Hz/s

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