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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 toward this parked car, pass it, and drive away, you observe the frequency to change by 75 Hz. At what speed are you driving

Respuesta :

Answer: [tex]13.4\ m/s[/tex]

Explanation:

Given

The frequency of the source is [tex]f_o=960\ Hz[/tex]

Change in frequency is [tex]75\ Hz[/tex]

Speed of sound [tex]c=343\ m/s[/tex]

Suppose [tex]v[/tex] is the velocity of the observer

Doppler frequency is given by

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

Here, the source is at rest

While approaching source, frequency is

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

While leaving, frequency is

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

The difference in the frequency is

[tex]\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[/tex]

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