Calculating Wavelength and Speed of a Standing Wave on a String

[Mirth]

Hey guys and girls, I'm having a hard time trying to start this problem. I think I have an idea of what to do to start it, but I'd like someone to verify it for me:

Homework Statement

A mass, m = 5.50kg hangs from a cord around a light pulley. The distance between point P and the pulley is L = 2.50m as shown.

[PLAIN]http://img341.imageshack.us/img341/4052/problemrm.jpg

(a) When the vibrator is set to a frequency of 120Hz, a standing wave with six loops is formed as shown below. Find the wavelength of this standing wave.
(b) Find the speed of the wave on the string
(c) Find the mass per unit length of the string.
(d) How many loops (if any) will result if the hanging m is changed to m'=22kg?

Homework Equations

1) Wavelength:
λ=f*v ( wavelength = frequency * speed)

2) Speed of a Wave on a string:
v= SqRt(F/[m/L]) ( speed = SqRt(Tension/[mass/Length]) ) (or m\L is linear density?)

3) String fixed on both ends:
f = (n * v)/(2*L) where n = 1,2,3,4 (frequency = (harmonic[6?] * speed)/(2 * Length)

The Attempt at a Solution

(a)
So I can't use equation 1 because I don't know the speed (which is the question to part b, actually...).

I can't find the speed using equation 2 because I don't know the Tension(F), and I don't believe I have enough amount of info to find the Tension.

So, using equation 3, I think I can convert that equation so that I can find speed? (I haven't taken a math class in YEARS, so converting is the hardest part for me in physics)
v= (n*f)/(2*L)

= (6*120Hz)/(2*2.50m) = 144 m/s

Can anyone verify that?

that would make:
λ=f*v
= 120Hz*144m/s = 17280

Additionally,, I'm confused that, if they asked me to find the speed in part (b), then maybe using speed to find the wavelength in part (a) is wrong?

As for part (c), I have no clue. (d) I might be able to figure out...


Any help would be greatly appreciated!

 

[Doc Al]

Homework Equations

1) Wavelength:
λ=f*v ( wavelength = frequency * speed)

This equation is incorrect. It should be:
v = f*λ

Hint for (a): Use the diagram!

 

[Mirth]

This equation is incorrect. It should be:
v = f*λ

Hint for (a): Use the diagram!

Ack, you're right, I didn't catch that. Thanks!

So... even if I didn't goof up on that, my thought process is still wrong it seems, if you're hinting at me using the diagram. Hmmm... I really shouldn't have waited so many years to take Physics II, as there is probably a formula from Physics I that I have forgotten... The diagram has mass and I guess gravity on the mass, but I'm not sure if those would help me...

 

[Doc Al]

Another hint: Mark off one wavelength on the diagram. How long is it?

 

[Mirth]

Another hint: Mark off one wavelength on the diagram. How long is it?

Oooh. I hope I get on base with this, but if I recall from the lecture correctly, one loop is half a wavelength. I have six loops, so it'd be 3 wavelengths?

 

[Doc Al]

Oooh. I hope I get on base with this, but if I recall from the lecture correctly, one loop is half a wavelength. I have six loops, so it'd be 3 wavelengths?

Now you're on track.

 

[Mirth]

Thanks a bunch, I was definitely over-thinking that one. :D

So, for (b), it'd simply be :
v = 120Hz * 3
= 360 m/s ?

 

[Doc Al]

So, for (b), it'd simply be :
v = 120Hz * 3
= 360 m/s ?

Where did you get the 3? What's the wavelength again?

 

[Mirth]

Where did you get the 3? What's the wavelength again?

Now I'm confused again :( I thought we determined the wavelength was half of six, being 3?

Edit:
Ah. I think it'd be wavelength = 2.5m/(6/2) = 0.83?

 

[Doc Al]

Edit:
Ah. I think it'd be wavelength = 2.5m/(6/2) = 0.83?

That's the one.