Physics Help =[ I Dont understand this =[?

Question

Okay i have three problems that I cant seem to be able to do. For some reason i cant do this. Well here are the problems. can someone help me?

1. The whistle on a train has a frequency of 440 Hz. The train is moving at 35.0 m/s toward a person standing on the platform. If sound travels at 345 m/s, what is the wavelength of the sound heard by the person?


2. An auto with a siren having a frequency of 365 Hz is approaching a stationary detector at a speed of 75 km/h. What is the frequency of the siren appear to be if sound travels at 345 m/s?

**For those two, the doppler shift equation is to be used right? But i dont understand how to do it.**

3. A pipe open at both ends is 55 cm long. What are the wavelenghts of the fundamental and the first three overtones?

So i really need help on these problems! If anyone can help me than i would be realllly grateful!

Answer 1

The equation for the doppler shift, expressed in _wavelength_ is given for wavelength L as:
Ls = Shifted Wavelength
Lo = Original Wavelength

Ls = Lo ( 1 + v/c )

Where v is the relative velocity of the two objects in question, (emitter & listener,) and c is the speed of sound. (The term 'c' also refers to the speed of light in an identical equation for the doppler shift in _light_.)

So we know whta the frequency is, 440 Hz, and we know the speed of sound, 345 m/s. Therefore we can solve for the original wavelength.

c = L * v (here v is frequency.)
L = c/v = (345 m/s) / (440 1/s) = 0.784 m = 78.4 cm

Lo = 78.4 cm

Now, it's the straightforward matter of plugging into the doppler equation:

Ls = Lo ( 1 + v/c )
Ls = (78.4 cm) ( 1 + (-35 m/s)/(345m/s) )
Ls = (78.4 cm) ( 1 - 0.1015 ) = 78.4 * ( 0.8985 )
Ls = 70.4 cm

The only tricky bit here is the SIGN of the velocity. It's NEGATIVE because the source is _approaching_ the listener, so the wavelength must be _shorter_. The only way to make that happen is if the term (1+v/c) is less than one, meaning that since the speed of sound is a constant and is positive, we must make the incoming velocity negative. Another way of putting it: Approaching objects cause the distance between them to grow _less_ with time, therefore the velocity if negative.

For problem #2, it's the same principle:

Lo = c/v = 94.5 cm
Ls = (94.5 cm)( 1 + (-75)/(345) ) = 94.5 * ( 0.783 )
Ls = 74.0 cm

Problem #3 is even simpler than the other two:

Fundamental frequency is the frequency at which the lenght of the pipe is ONE HALF the length of the pipe. So it's another case where you solve for one term in the equation:

c = L * v

And then you determine the other terms from that one term.

Solving for the fundamental frequency:

55 cm = 1/2 * L
L = 110 cm = 1.1 m

v = c / L = 345 m/s / 1.1 m = 313.6 Hz

The next 3 overtones are where the pipe's length is TWO HALVES of the wavelength, THREE HALVES of the wavelength, and FOUR HALVES of the wavelength. So the pipe doesn't change, but the wavelength gets shorter.

L1 = 55 cm
L2 = 36.7 cm
L3 = 27.5 cm

v1 = 627.2 Hz
v2 = 940.1 Hz
v3 = 1254.5 Hz

Easy-peasy.

Answer 2

The doppler equation is, apparently:

f(apparent) = [v/(v - v(1))]f,
where:
f(apparent) is the frequency of the sound heard by the person
v is the velocity of the emitted sound-wave
v(1) is the velocity of the train

So, f(apparent) =[345/(345 -35)](440) = 490 Hz.

Then, frequency x wavelength = speed of sound.
345 m/s = 490 x wavelength. So,
wavelength = 345/490 = 0.70 m.

2. Use the same equation in the same way.
3. The fundamental frequency is the longest wave that'll fit in the pipe- 55cm.
The next overtone is (I think), half that: 55/2
The next one is then 55/3, then 55/4 etc.