Question

A car horn creates a 595 hz tone

at rest. two cars pass on the
street, each going 20.0 m/s; the
first car honks. what frequency
does the other car hear after they
pass each other?
(speed of sound = 343 m/s)
(unit = hz)

Answer 1

Answer: 669 Hz

Step-by-step explanation:

The frequency, f', at which the other car hears the honk is what we have to find. We do this by using the equation for the Doppler effect,

`f' = \left( (v+v_o)/(v-v_s) \right)f`

Where:

• 
  `f =\rm 595\ Hz` is the frequency of the horn

• 
  `v =\rm 343\ m/s` is the speed of sound

• 
  `v_s =\rm 20.0\ m/s` is the speed of the first car

• 
  `v_o =\rm 20.0\ m/s` is the speed of the other car

We proceed with the solution,

`\displaystyle f' &= \left( (v+v_o)/(v-v_s) \right)f\\[0.3cm] &=\rm \left( (( 343\ m/s)+(20.0\ m/s))/(( 343\ m/s)-(20.0\ m/s)) \right)( 595\ Hz)\\[0.3cm] &\approx\boxed{\rm 669\ Hz}`