Question

You're driving your new Corvette convertible and can clearly hear other cars driving nearby. One of these cars honks their horn and your car, with its apps and sensors, displays the horn sound as 760Hz. Your Corvette also registers the car as a Mustang with a car horn of 795Hz. You are stopped at a stop light when their horn blares. Another of your Corvette apps measures the air temperature to be 26°C. a) What is the speed of sound in this air? b) How fast is the Mustang driving relative to you? c) Is the Mustang driving toward or away from you? d) The stop light turns green and you quickly reach 20 m/s. The Mustang's horn appears broken as it continues to sound and the frequency app measures a lower value than before. What is the new frequency displayed and are you driving toward or away from the Mustang? e) You decide you like the Mustang's horn sound so you change the Corvette to emit the 795Hz. What frequency do you hear from your car as you drive at 20 m/s?

Answer 1

a) The formula for dependence of sound velocity on temperature is -

  $V=331+0.6\times T$ [T is measured in degree centigrade]

So putting the value T=26, we get V= 346.6 m/s

b) The normal frequency of Mustang is 795 Hz and it appears 760 Hz(appears less) to you. The formula for doppler shift is -

$f=(\frac{V}{V+v_{s}}) f_{0}$ [where f is the observed frequency and $f_{0}$ is the actual frequency and $v_{s}$ is velocity of the sound source (here it is Mustang)]

Putting f=760 Hz and $f_{0}$ = 795 Hz and V=346.6 m/s,

We get $v_{s}$ = 15.96 m/s. So the velocity of the Mustang relative to you is 15.96 m/s.

c) As the frequency appears lesser to you, the Mustang is driving away from you.

d) Now, as the frequency appears lower than normal you are driving away from the Mustang. The formula for doppler shift is -

$f=(\frac{V-v_{0}}{V})f_{0}$ [where $v_{0}$ is the velocity of observer and the rest symbols bear the same meaning as earlier. ]

Putting $v_{0}$ = 20 m/s , V= 346.6 m/s and $f_{0}$ = 795 Hz, we get f=749.13 m/s.

e) As you are sitting in the car and the velocity of the car is 20 m/s, you are also going with a velocity of 20 m/s. So relative velocity of you w.r.t the car is zero. So the frequency will be the same(795 Hz) for you