# Question on a waves/sound problem

• Kalix
In summary, the problem involves two strings at different lengths and linear densities that are joined together and stretched with a tension of 190.0 N. The goal is to find the lowest frequency that allows standing waves with a node at the junction. The equations to be used are f=nv/2L and (n1v1)/2L1=(n2v2)/2L2, and the given information includes the lengths, densities, and unknowns of the strings. The attempt at a solution involves plugging in the given variables into the second equation and solving for a ratio between n1 and n2, but the individual values of v and n are still unknown.
Kalix

## Homework Statement

Question: Two strings at different lengths and linear densities are joined together. They are stretched so that the tension in each string is 190.0 N. The free ends are fixed in place. Find the lowest frequency that permits standing waves in both strings with a node at the junction. The standing wave pattern in each string may have a different number of loops.

## Homework Equations

3.75 m 1.25m
_________________=====================

6*10^-2 kg/m 1.5*10^-2 kg/m

(this is kinda what the picture looks like if it helps but it seems really confusing on the computer)

Equations I should use (there may be others):
f=nv/2L
(n1v1)/2L1=(n2v2)/2L2

Other information I am given:
L1=3.75
L2=1.25
n1=?
n2=?
v1=?
v2=?
(m/L)=6.00x10^-2 kg/m
(m/L)2=1.50x10^-2 kg/m

I need to create a ratio between n1 and n2.

I don’t understand how I get v and then how to find a ratio between n1 and n2.

## The Attempt at a Solution

Well above I listed all the variables I knew and the ones I didn't know. from that I plugged what I had into the second equation and got (n1v1)/2(3.75)=(n2v2)/2(1.25). That is about how far I got. I don’t understand how I get v and then how to find a ratio between n1 and n2.

Sorry the picture got a little messed up on the computer. Hopefully it will be easy to tell where things go based on the other information.

## 1. What is the relationship between waves and sound?

Waves are a form of energy that travel through a medium, such as air or water. Sound is a type of wave that is created by vibrations in the medium, and it travels in all directions from its source.

## 2. How do waves affect the speed of sound?

The speed of sound is dependent on the properties of the medium it is traveling through, such as temperature and density. In general, sound travels faster in denser mediums, such as water, compared to less dense mediums, such as air.

## 3. What is the difference between longitudinal and transverse waves?

Longitudinal waves are waves in which the particles of the medium vibrate in the same direction as the wave is traveling, while transverse waves are waves in which the particles vibrate perpendicular to the direction of the wave.

## 4. How does wavelength affect the pitch of sound?

The pitch of sound is determined by its frequency, which is the number of waves that pass by a certain point in a given amount of time. A shorter wavelength, or higher frequency, results in a higher pitch sound, while a longer wavelength, or lower frequency, results in a lower pitch sound.

## 5. Can sound waves travel through a vacuum?

No, sound waves require a medium to travel through. In a vacuum, there is no medium for the sound waves to vibrate and therefore, they cannot travel.

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