Question

A 50.0 Watt stereo emits sound waves isotropically at a wavelength of 0.700 meters. This stereo is stationary, but a person in a car is moving away from this stereo at a speed of 40.0 m/s. The frequency of sound waves that the car receives is ________. In addition, when the car is 70.0 meters away from the speaker, the car will hear sound waves with a sound intensity level of _________ .

Answer 1

Answer:

a) f' = 432 Hz

b) I = 8.12*10^-4 W/m^2

Explanation:

a) To calculate the frequency of sound waves that car receives, you take into account the Doppler effect. In this case (observer moves away of the source) you have the following formula:

$f'=f(\frac{v-v_o}{v+v_s})$    (1)

where

f: frequency of the source = ?

v: speed of sound = 343 m/s

vo: speed of the observer = 40.0 m/s

vs: speed of the source = 0 m/s (stationary)

You replace the values of all parameters in the equation (1):

To calculate f' you first calculate the frequency of the sound wave, by using the following formula:

$v=\lambda f$

v: speed of sound

λ: wavelength = 0.700 m

$f=\frac{v}{\lambda}=\frac{343m/s}{0.700m}=480Hz$

Next, you replace the values of all parameters in the equation (1):

$f'=(490Hz)(\frac{343m/s-40.0m/s}{343m/s})=432Hz$

hence, the frequency perceived by the car is 432 Hz

b) To calculate the power of the sound wave, when the car is 70.0 maway from the speaker, you use the following formula:

$I=\frac{P}{4\pi r^2}$

P: power of the source = 50.0 W

r: distance to the source = 70.0 m

$I=\frac{50.0 W}{4\pi(70.0m)^2}=8.12*10^{-4}\frac{W}{m^2}$

hence, the intensity is 8.12*10^⁻4 W/m^2