Question on a waves/sound problem

  • Thread starter Thread starter Kalix
  • Start date Start date
AI Thread Summary
To solve the problem of finding the lowest frequency for standing waves in two strings with different lengths and linear densities, the tension in both strings is given as 190.0 N. The relevant equations include the wave frequency formula f = nv/2L and the relationship between the frequencies and modes of the two strings. The user has identified the lengths and linear densities of the strings but is struggling to calculate the wave speeds (v1 and v2) and establish a ratio between the mode numbers (n1 and n2). The user has made progress by setting up the equation relating the two strings but needs guidance on deriving the wave speeds and the mode number ratio. Understanding these concepts is crucial for determining the lowest frequency that allows for standing waves with a node at the junction.
Kalix
Messages
26
Reaction score
0

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.
 
Physics news on Phys.org
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.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top