How Do You Calculate the Frequency of a Wave Traveling Along a String?

[kel]

Hi

I have a question that I'm not sure how to answer, it goes like this:

A string along which waves can travel in 2.7m long and has a mass of 260g. The tension is 36N. What must the frequency of a traveling wave of amplitude 7.70mm be if the average power transmitted is 85W?

I was going to use the average power question and worked out that the linear density would be 0.96 (or 9.6e-3), but I'm not sure how to go about finding the angular frequency or height of the wave (e.g. y) with the info given in the question or am I going about this in completely the wrong fashion?

Also, where is the equation editor in this forum? I was going to write out the Power equ' but it would look fairly untidy in normal text.

Thanks

 

[kel]

Just realized the height (y) is the amplitude squared - which I work out to be:

7.7mm = 7.7e-3 m, so that squared should be 5.929e-5, I think.

If this is correct then I just need the velocity and angular wavelength.

 

[kel]

ok, slight update. I have now worked out that the linear density is in fact 0.096 and the amplitude is 7.7e-3

Could anyone tell me how I get the velocity from this? I mean the speed of the wave v
(p=1/2*linear density*v*w^2*y^2)
Thanks

 

[Hootenanny]

The velocity on a wave can be obtained using the equation;

v = \sqrt{\frac{T}{\frac{m}{L}}}

This can be derrived from the wave equation

~H

 

[kel]

Thanks,
I just realized that I can use the root of tension/linear density.

and got a value of 19.36, does that sound about right?

 

[kel]

Aha !

How does this sound?

w^2= 85/0.5*(0.096)*19.36*(7.7e-3)^2
w^2= 1542733.411
w = root of the above = 1242 rad/s
f = w/2pi = 197.67 Hz

 

[Hootenanny]

and got a value of 19.36, does that sound about right?

I would agree with that.

~H

 

[kel]

HOOOOORRRAYYYY!

Hey are you any good with wave interference? My lecturer has been crafty and given us a question where I have 2 waves which interfere, but the only equation given is that of the resultant wave and I don't know how to resolve them back into their component waves.

I know it's along the lines of vector algebra, but I'm clueless on this one I'm afraid.

 

[Hootenanny]

Aha !

How does this sound?

w^2= 85/0.5*(0.096)*19.36*(7.7e-3)^2
w^2= 1542733.411
w = root of the above = 1242 rad/s
f = w/2pi = 197.67 Hz

I would also agree with that. Well done, you solved it without any help from me, I feel reducntant now . By the way, to insert mathematical equations see this thread; https://www.physicsforums.com/showthread.php?t=8997 . Also, if you click on any formulae in these forums a pop up will present the code used to produce the equation.

~H

 

[Hootenanny]

HOOOOORRRAYYYY!

Hey are you any good with wave interference? My lecturer has been crafty and given us a question where I have 2 waves which interfere, but the only equation given is that of the resultant wave and I don't know how to resolve them back into their component waves.

I know it's along the lines of vector algebra, but I'm clueless on this one I'm afraid.

If you post your question I guarantee someone on PF will be able to answer it

~H

 

[kel]

Cheers! I'm sure I owe u a few beers by now tho!

 

[Hootenanny]

Cheers! I'm sure I owe u a few beers by now tho!

Not a problem my friend . Damn, this virtual beer sure does taste good

~H