Same string, different mass per unit length, whats the wavelength?

[bobbo7410]

[SOLVED] Same string, different mass per unit length, what's the wavelength?

*oddly I can't edit the original title?

Homework Statement

A string is made of two materials of different mass per unit length. On the left side of the string, the mpu is given as well as its wavelength. On the right only the mpu. The question asks for the right side's wavelength.

Homework Equations

xxx

The Attempt at a Solution

I immediately began doing just a simple balancing equations. 2.76/20.4 = 3.63X

yet it returned the answer as incorrect. How can that be??

as well, I thought maybe it was trick question since its all the same single string, the wavelength must be the same. so I put 20.4 and as well it returned it as incorrect.

I'm really not sure what I did wrong.

 

[Doc Al]

How does the wavelength (or wave speed) depend on the mass per unit length?

 

[bobbo7410]

Not sure if you were questioning me or you stating the problem variables don't depend on one another.

mu (mpl or mass per unit length) = string mass / string length

v = square root of (T / mu) where t = mg

thats all I can really find or think of regarding mu

 

[Doc Al]

v = square root of (T / mu) where t = mg

Good. The square root is key. That's what you were missing earlier.

 

[bobbo7410]

? earlier all i had was a simply balanced equation that's it.

v = square root (T/mg) T being the period and mg being mass * gravity

I don't know T, or the mass.

perhaps you could break it down a little more basic for me.

Thanks for the help!

 

[Doc Al]

? earlier all i had was a simply balanced equation that's it.

Your balance equation was incorrect. Come up with a new one using the equation for wave speed.

v = square root (T/mg) T being the period and mg being mass * gravity

I thought we agreed that: v = square root (T/mu)
You don't need to know the tension, since it's the same for both sides of string.

Combine this with the "wave equation": v = f * wavelength. (Hint: The frequency is also the same for both sides.)

 

[bobbo7410]

: ) thank you! that made it much simpler for me, I got it correct.

for some reason I looked back and the mu looked like mg.

So basically:

v = square root (T / mu)
v = f * wavelength

so [ f * wavelength = square root ( T / mu ) ]

I set the frequency to 1 for both so I only had 1 variable to determine. I solved for T on the left side of the string and once I found that I used that same T to determine the wavelength for the right side.

yey thanks doc

 

[bobbo7410]

https://www.physicsforums.com/showthread.php?p=1597041#post1597041

for my first equation.. Would it be beneficial to use the same setup as above to solve for frequency or T?

because if I were to find either of those I could easily find the velocity. yet I think am back where I started (2 unknown variables) since I can't simply substitute 1 for the frequency in that problem.