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djyliett [7]
3 years ago
5

g Two cars, car 1 and car 2 are traveling in opposite directions, car 1 with a magnitude of velocity v1=13.0 m/s and car 2 v2= 7

.22 m/s. If car 1’s exhaust system is loud enough to be heard by car 2 and the frequency fe produced from the exhaust is 2.10 kHz. What frequencies would be heard by car 2 when the cars are approaching, passing, and retreating from one another?
Physics
1 answer:
bogdanovich [222]3 years ago
7 0

Answer:

When they are approaching each other

    f_a = 2228.7 \  Hz

When they are passing  each other

    f_a = 2100Hz

 When they are retreating  from each other

     f_a =  1980.7 Hz

Explanation:

From the question we are told that

     The velocity of car one is  v_1 = 13.0 m/s

      The velocity of car two is  v_2 = 7.22 m/s

     The frequency of sound from car one is  f_e = 2.10 kHz

Generally the speed of sound at normal temperature is  v = 343 m/s

  Now as the cars move relative to each other doppler effect is created and this  can be represented  mathematically  as

              f_a = f_o [\frac{v \pm v_o}{v \pm v_s} ]

Where v_s is the velocity of the source of sound

            v_o is the velocity of the observer of the sound

            f_o is the actual frequence

             f_a  is the apparent frequency

Considering the case when they are approaching each other

        f_a = f_o [\frac{v +  v_o}{v -  v_s} ]

          v_o = v_2  

         v_s = v_1

         f_o = f_e

Substituting value

            f_a = 2100  [\frac{343 +  7.22}{ 343  -  13} ]

              f_a = 2228.7 \  Hz

Considering the case when they are passing  each other    

At that instant

                  v_o = v_s = 0m/s

                   f_o = f_e

               f_a = f_o [\frac{v }{v } ]

              f_a = f_o

Substituting value

             f_a = 2100Hz

Considering the case when they are retreating  from each other    

                f_a = f_o [\frac{v -  v_o}{v +   v_s} ]

          v_o = v_2  

         v_s = v_1

         f_o = f_e      

Substituting value

         f_a = 2100  [\frac{343 -  7.22}{343 +   13} ]    

          f_a =  1980.7 Hz    

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