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

• bobbo7410
In summary, the conversation discusses a problem involving a string made of two materials with different mass per unit length. The task is to find the wavelength on the right side of the string, given the information on the left side. The solution involves using the equations for wave speed and frequency, and making use of the fact that these values are the same on both sides of the string. The conversation also includes a discussion on balancing equations and using the correct variables in calculations.
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.

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.

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

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

bobbo7410 said:
v = square root of (T / mu) where t = mg
Good. The square root is key. That's what you were missing earlier.

? 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!

bobbo7410 said:
? 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.)

: ) 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

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.

Last edited:

## 1. How does the mass per unit length affect the wavelength of a string?

The mass per unit length of a string affects the wavelength by changing the speed of the wave traveling through the string. A higher mass per unit length will result in a slower wave speed and a longer wavelength, while a lower mass per unit length will result in a faster wave speed and a shorter wavelength.

## 2. Is the wavelength of a string with the same mass per unit length always the same?

No, the wavelength of a string with the same mass per unit length can vary depending on other factors such as tension, material, and length of the string. Mass per unit length is just one factor that affects the wavelength.

## 3. Can the wavelength of a string be calculated using the mass per unit length?

No, the wavelength of a string cannot be calculated using just the mass per unit length. Other factors such as tension and material properties also need to be considered in order to accurately calculate the wavelength.

## 4. Does increasing the mass per unit length always result in a longer wavelength?

Not necessarily. While increasing the mass per unit length will generally result in a longer wavelength, other factors such as tension can also affect the wavelength. Additionally, if the tension is kept constant, increasing the mass per unit length may actually decrease the wavelength.

## 5. How does the mass per unit length affect the frequency of a string?

The mass per unit length of a string does not directly affect the frequency. However, it does affect the wave speed, which in turn affects the frequency. A higher mass per unit length will result in a slower wave speed, leading to a lower frequency, and vice versa.

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