A driver of a car travelling with a speed 30m/s towards a hill souns a horn of frequency 600Hz.if the velocity of sound in air is 330m/s.calculate the frequency of reflected sound as heard by the driver?
The frequency of the reflected sound as heard by the driver can be calculated using the formula:
f' = (v +/- vD)/(v +/- vS) * f
where:
f = 600 Hz (frequency of the horn)
v = 330 m/s (velocity of sound in air)
vD = 30 m/s (velocity of the car towards the hill)
vS = -v (velocity of the reflected sound)
+/- means to use the plus sign if the listener is moving towards the source, and minus if moving away from the source
Substituting the values, we get:
f' = (330 + 30)/(330 - 330) * 600
f' = 660/0 * 600
f' = undefined
This means that the reflected sound cannot be heard by the driver, as it does not reach their ears.
To calculate the frequency of the reflected sound as heard by the driver, we can use the Doppler effect formula:
f' = f((v + vd) / (v + vs))
Where:
f is the original frequency (600 Hz)
v is the velocity of sound in air (330 m/s)
vd is the velocity of the driver (30 m/s)
vs is the velocity of the source (in this case, the reflected sound) relative to the medium (air) - which is what we need to find
Let's calculate the frequency of the reflected sound:
f' = 600 * ((330 + 30) / (330 + vs))
Next, let's rearrange the equation to solve for vs:
(330 + vs) = (330 + 30) / (f'/f)
vs = (330 + 30) / (f'/f) - 330
Plugging in the values:
vs = (360 / (f'/f)) - 330
Finally, we can substitute f' (frequency of reflected sound) for f' = f = 600 Hz:
vs = (360 / (600/600)) - 330
vs = (360 - 330)
vs = 30 m/s
Therefore, the frequency of the reflected sound as heard by the driver is the same as the original frequency, which is 600 Hz.