The siren in an ambulance has a frequency (according to you) of 1100 hz as it moves towards you at a speed v. It then makes a u-turn and travels away from you with a speed v, and you hear a frequency of 950 hz. What is the final speed v of the siren?
25.0 m/s
To find the final speed (v) of the siren, we can use the Doppler effect equation for sound waves. The formula for the observed frequency (f) of a moving source, relative to an observer, is given by:
f = f0 * (v + vo) / (v - vs)
Where:
- f is the observed frequency
- f0 is the original frequency emitted by the source (in this case, 1100 Hz)
- v is the speed of sound in the medium (assumed to be constant)
- vo is the speed of the observer
- vs is the speed of the source
In this scenario, we have two different cases:
1. The siren is moving towards you, so the observed frequency is 1100 Hz.
2. The siren is moving away from you, so the observed frequency is 950 Hz.
Let's solve these equations separately to find the values of vo (your speed) and vs (the siren's speed):
Case 1: Moving towards you (f = 1100 Hz)
1100 = 1100 * (v + vo) / (v - vs)
Simplifying the equation:
(v - vs) / (v + vo) = 1
Case 2: Moving away from you (f = 950 Hz)
950 = 1100 * (v + vo) / (v - vs)
Simplifying the equation:
(v - vs) / (v + vo) ≈ 1.158
Since vs is the same in both cases, we can equate the two expressions for (v - vs) / (v + vo):
(v - vs) / (v + vo) = (v - vs) / (v + vo) ≈ 1.158
Now, solve for v:
1 = 1.158
This is not possible mathematically, indicating an error in the problem statement or calculations. Please double-check the values or provide additional information to proceed with finding the final speed (v) of the siren.