Driving down a quiet street on a summer day with the car windows down, you see a convertible approaching from the opposite direction, with the driver playing her car stereo loudly. Having a well-trained musician’s ear, you notice that the song you hear is in a key one semitone (the interval between two adjacent keys on a piano) above the key in which the song is typically heard. You also know that to shift any note by one semitone, the frequencies must be related by a factor of 1.06. Assume both drivers are traveling at the same speed, what is their speed?

The ratio of apparent frequency and real frequency is 1.06 . Let v be their velocities . According to Doppler formula for source of sound and observer

approaching each other , the formula is as follows

n = n₀ ( V+v ) / (V-v )

Here V is velocity of sound which is 340 m /s

n / n₀ = ( V+v ) / (V-v )

1.08 = [tex]\frac{( V+v\\)}{(V-v)}[/tex]

360.4 - 1.06 v = 340 +v

v = 9.9 m /s.