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goldenfox [79]
2 years ago
8

The security alarm on a parked car goes off and produces a frequency of 960 Hz. The speed of sound is 343 m/s. As you drive towa

rd this parked car, pass it, and drive away, you observe the frequency to change by 75 Hz. At what speed are you driving
Physics
1 answer:
Greeley [361]2 years ago
7 0

Answer: 13.4\ m/s

Explanation:

Given

The frequency of the source is f_o=960\ Hz

Change in frequency is 75\ Hz

Speed of sound c=343\ m/s

Suppose v is the velocity of the observer

Doppler frequency is given by

f'=f_o\left(\dfrac{c\pm v_o}{c\pm v_s}\right)

Here, the source is at rest

While approaching source, frequency is

f_1=f_o\left(\dfrac{c+v}{c}\right)\quad \ldots(i)

While leaving, frequency is

f_2=f_o\left(\dfrac{c-v}{c}\right)\quad \ldots(ii)

The difference in the frequency is

\Rightarrow f_1-f_2=75\\\\\Rightarrow f_o\left(\dfrac{c+v}{c}\right)-f_o\left(\dfrac{c-v}{c}\right)=75\\\\\Rightarrow f_o\left(\dfrac{2v}{c}\right)=75\\\\\Rightarrow v=\dfrac{75\times 343}{2\times 960}\\\\\Rightarrow v=13.39\approx 13.4\ m/s

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