two cars are heading at each other with the same speed v. The horn of one (f=3000Hz) is blowing,and is heard to have a frequency of 3400Hz by the people in the other car.Find v if the speed of sound is 344m/s
Review the formulas presented here:
In your case the source moves the observer AND the observer moves toward the source. The true frequency in still air is fo = 3000. The received frequency is 3400.
The received frequency is
f = fo*(344+V)/(344-V)
(344+V)/(344-V) = f/fo = 11.333
Solve for V
To find the speed (v) of the cars, we can use the Doppler effect equation for sound waves:
Δf/f = v/c
Where:
Δf = change in frequency (in Hz)
f = original frequency of the sound (in Hz)
v = velocity of one of the cars (in m/s)
c = velocity of sound in air (in m/s)
We are given:
f = 3000 Hz (frequency of the horn)
Δf = 3400 Hz - 3000 Hz = 400 Hz (change in frequency)
c = 344 m/s (velocity of sound in air)
Substituting the given values into the equation, we have:
400 Hz / 3000 Hz = v / 344 m/s
Let's solve for v:
v = (400 Hz / 3000 Hz) * 344 m/s
v = (4/30) * 344
v = 45.87 m/s (rounded to two decimal places)
Therefore, the speed of each car is approximately 45.87 m/s.