1)As a sound source moves away from a stationary observer, the number of waves will.
A)increase
B)decrease
C)remain the same
D)need to know the speed of the source
(answer:decrease.) As the detector recedes from the source, the relative velocity is smaller, resulting in a decrease in the wave crests reaching the detector each second. (thats from the book)
2)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 agree with the book, the number of waves per second (which is frequency) decreases. I am still not certain of the poor wording of the question.
2. I will be happy to critique your calcs.
2.88% times 343
= 9.8784 I don't understand this one b/c the doppler equation doesnt work
actually, it does. And, you just used the approximate solution in your argument.
F/fo= 343/(343-v)= 1/(1-v/343) or
1-v/343=1/1.0288
solve for v. As I recall, this is one of your choices.
drwls already worked it out for me,I found it on another page. answer is 9.6 m/s
good. I hope you understand how it is worked.
To solve this problem, we can use the Doppler effect equation for sound frequency:
f' = (v + vd) / (v + vs) * f
Where:
- f' is the observed frequency
- v is the speed of sound
- vd is the velocity of the detector (observer)
- vs is the velocity of the source
- f is the source frequency
In this case, we want to find how fast the car should move toward you, so the observed frequency is 2.88% (or 0.0288) higher than the source frequency. Let's denote this observed frequency as f'.
First, we need to rearrange the equation to solve for vs:
vs = ((f' / f) - 1) * (v + vd)
Substituting the given values and solving for vs:
vs = ((1 + 0.0288) - 1) * (343 + 0)
vs = 0.0288 * 343
vs = 9.8744 m/s
Therefore, the car should move toward you at a speed of approximately 9.8744 m/s for the car's horn to sound 2.88% higher in frequency than when the car is stationary.