How fast should a car move toward you for the car's horn to sound 2.88% higher in frequency than when the car is stationary? The speed of sound is 343 m/s.
I don't know what equation to use. I think I'm suppose to use this:
fs(v-vd/v-vs)
I know I got it wrong I got 11.8 m/s
To solve this problem, you need to use the Doppler effect equation for sound:
f' = (v + vd)/(v + vs) * f
Where:
f' is the observed frequency (frequency heard)
f is the original (source) frequency
v is the speed of sound (given as 343 m/s)
vd is the velocity of the observer (car)
vs is the velocity of the source (car)
In this case, the car's horn sounds 2.88% higher in frequency. So, f' = f + 0.0288f.
Given that v = 343 m/s, you are looking for vd (velocity of the observer) when the frequency increases by 2.88%.
Now, let's rearrange the equation to solve for vd:
f' = (v + vd)/(v + vs) * f
f + 0.0288f = (v + vd)/(v + 0) * f
Simplifying the equation:
1.0288f = (v + vd)/v * f
1.0288 = (v + vd)/v
Now, let's solve for vd:
vd = 1.0288v - v
Given that v = 343 m/s, we can substitute this into the equation:
vd = 1.0288 * 343 m/s - 343 m/s
Calculating this, vd = 11.743 m/s (rounded to three decimal places)
Therefore, the car needs to move toward you with a velocity of approximately 11.743 m/s for the car's horn to sound 2.88% higher in frequency than when the car is stationary.
To determine the speed at which a car should move towards you for its horn to sound 2.88% higher in frequency than when it is stationary, you can use the Doppler effect formula for sound:
fs = fo * (v + vd) / (v + vs)
Where:
- fs is the observed frequency
- fo is the original frequency
- v is the speed of sound
- vd is the velocity of the detector (the observer)
- vs is the velocity of the source (the moving car)
In this case, the observed frequency is 2.88% higher than the original frequency, which means fs = fo + 0.0288 * fo = 1.0288 * fo.
Given that the speed of sound (v) is 343 m/s, and the velocity of the detector (vd) is 0 m/s (since you are stationary), the equation becomes:
1.0288 * fo = fo * (343 + vs) / (343)
Now we can simplify the equation:
1.0288 = (343 + vs) / 343
Multiply both sides of the equation by 343:
1.0288 * 343 = 343 + vs
352.8684 - 343 = vs
vs = 9.8684 m/s
Therefore, the car should be moving towards you at a speed of approximately 9.87 m/s for its horn to sound 2.88% higher in frequency.