This is in reply to a previous post, I'm not really sure whether replies to posts that are several days old are viewed by anyone, so I'm reposting just in case.

In reply to bobpursley's post,
I just want to ask, how would you know how long it takes for the sound to reach you? Would you multiply the time it took for the frequency to decrease by 2, to find the total time?

Homework Help Forum: Physics - Frequency

Posted by Intensity on Monday, January 25, 2010 at 8:43pm.

While blowing its horn of frequency 580 Hz, a car accelerates at 0.4 m/s2.

The car starts from rest by your side and moves away.

How long will it take for the frequency you hear to decrease by 5%?

Hint: Do not forget to include the time it will take for sound to reach you.

* Physics - Frequency - bobpursley, Monday, January 25, 2010 at 8:47pm

figure the velocity the car has to go to drop the sound by 5Percent. then, figure the time to get to that speed, then add the time it takes sound to travel that same distance back to you.

time sound to travel= distance/velocitysound

time for train get to the speed of v

v=V0+at
solve for t.

How long will it take for the frequency you hear to decrease by 5%?

This is what I have done so far:
I found the speed of the car by using this equation:

f2=f1(340/340+Vsource) ; f2/f1 = 0.95 (..since the frequency is decreasing by 5%)

Next, I used this speed and the acceleration given to find the time it took for the frequency to decrease this much.

From what you are saying above I understood that you wanted me to find the distance the car travelled during this time and use that distance to see how long it took the sound to reach us?

This is what I ended up using, but I don't think it's right.

(V2)^2 = (V1)^2 + 2ad

t = d/V ; where V = 340 and t was my final asnwer..

I think that since we're talking about a wave and its parameters as the sound reaches us; my method would be inappropriate?

Please help if it's possible!

To find the total time it will take for the frequency you hear to decrease by 5%, you need to consider both the time it takes for the car to reach the required velocity and the time it takes for the sound to travel back to you.

First, let's find the velocity the car needs to reach to decrease the frequency by 5%. We can do this by using the Doppler effect equation:

f' = ((v + vd) / (v + vs)) * f

Where:
f' is the observed frequency
v is the speed of sound
vd is the velocity of the car
vs is the velocity of the source (which is 0 in this case since the car is moving away from you)
f is the original frequency (580 Hz)

Rearranging the equation to solve for vd:

vd = ((f' / f) - 1) * v

Substituting the given values, where f' = f - (0.05f) = 0.95f and v = speed of sound:

vd = ((0.95 * 580) / 580) * v

Next, we find the time it takes for the car to reach this velocity. We can use the formula:

v = u + at

Where:
v is the final velocity (vd)
u is the initial velocity (0 since the car starts from rest)
a is the acceleration (0.4 m/s^2)
t is the time it takes to reach the final velocity

Rearranging the equation to solve for t:

t = (v - u) / a

Substituting the given values:

t = (vd - 0) / 0.4

Now, we know the time it takes for the car to reach the required velocity. To find the total time, we also need to consider the time it takes for sound to travel back to you. The time it takes for sound to travel is given by:

time = distance / speed

The distance the sound has to travel is the same as the distance the car has traveled, which is the average velocity of the car multiplied by the total time it took for the car to reach that velocity:

distance = (0 + vd) / 2 * t

Substituting the values we have:

distance = (0 + vd) / 2 * ((vd - 0) / 0.4)

Finally, we can calculate the time it takes for sound to reach you:

time_sound = distance / v

Substituting the values we have:

time_sound = ((0 + vd) / 2 * ((vd - 0) / 0.4)) / v

To find the total time, you can add the time it takes for the car to reach the velocity and the time for sound to travel back to you:

total_time = t + time_sound

By following these calculations, you will be able to find the total time it will take for the frequency you hear to decrease by 5%.