While sitting in your car by the side of a country road, you see your friend, who happens to have an identical car with an identical horn, approaching you. You blow your horn, which has a frequency of 260 Hz; your friend begins to blow his horn as well, and you hear a beat frequency of 5.0 Hz. Part A How fast is your friend approaching you

-6.49 m/s

Explanation:

This is doppler effect.

The equation is;

F_l = [ (v + v_l) / (v + v_s) ]F_s

Where;

F_l is frequency observed by the listener

v is speed of sound

v_l is speed of listener

v_s is speed of source of the sound

F_s is frequency of the source of the sound

In this question, the source of the sound is the moving vehicle.

Thus;

F_l = F_beat + F_s

We are given beat frequency (f_beat) as 5 Hz while source frequency (F_s) as 260 Hz.

So,

F_l = 5 + 260

F_l = 265 Hz

Since listener is sitting by car, thus; v_l = 0 m/s

Thus, from our doppler effect equation, let's make v_s the subject;

v_s = F_s[ (v + v_l) / F_l] - v

Speed of sound has a value of v = 344 m/s

Thus;

v_s = 260[ (344 + 0) / 265] - 344

v_s = - 6.49 m/s

This value is negative because the source is moving towards the listener