A police car siren emits a sound wave with a frequency fs = 400 Hz and it is moving toward the wall at 25 /m/s. What frequency reflected from the wall does the driver of the police car hear ?
The speed of sound is 340 m/s.
first figure out what higher frequency the wall hears
that frequency emmitted from the wall toward the car at that frequency
then get the still higher frequency back at the car
To calculate the frequency of the sound wave reflected from the wall, we can use the formula for the Doppler effect:
f' = f * (v + vd) / (v + vs)
Where:
f' = Frequency observed by the driver of the police car
f = Frequency emitted by the siren (400 Hz)
v = Speed of sound (340 m/s)
vd = Speed of the driver of the police car towards the wall (25 m/s)
vs = Speed of sound towards the police car (0 m/s in this case, as the wall is stationary)
Plugging in the values:
f' = 400 * (340 + 25) / (340 + 0)
f' = 400 * 365 / 340
f' = 431.18 Hz (rounded to two decimal places)
Therefore, the driver of the police car hears a frequency of approximately 431.18 Hz.
To find the frequency reflected from the wall that the driver of the police car hears, we need to take into account the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave observed by an observer moving relative to the source of the wave.
In this case, the police car is moving towards the wall, which causes a change in the frequency of the sound wave heard by the driver.
The formula for the Doppler effect is given by:
f' = (v + vr) / (v + vs) * fs
Where:
f' is the observed frequency
v is the velocity of sound in the medium (in this case, 340 m/s)
vr is the velocity of the observer (in this case, the velocity of the driver of the police car)
vs is the velocity of the source (in this case, the velocity of the siren on the police car)
fs is the frequency of the source (in this case, 400 Hz)
Given that vr = 25 m/s, vs = 0 (since the siren is on the police car), and fs = 400 Hz, we can substitute these values into the formula:
f' = (340 + 25) / (340 + 0) * 400
Simplifying this equation will give us the desired frequency:
f' = 365 / 340 * 400
f' = 435.29 Hz
Therefore, the driver of the police car will hear a frequency of approximately 435.29 Hz reflected from the wall.
fi=f(v)/(v-vs)
fi=400(340m/s)/(340m/s-25)
fi=431.7Hz