Tension in a rope, wavelengths, etc. I

[somesmallkid]

Homework Statement

A rope is stretched between two vertical supports. The points where it is attached (P and Q) are fixed. The linear density of the rope, u, is 0.6kg/m, and the speed of the transverse waves on the rope is 12 m/s.

a. what is the tension in the rope?
b. with what frequency must the rope vibrate to create a traveling wave with a wave length of 4m?

The rope can support standing waves of lengths 4m and 3.2m, whose harmonic numbers are consecutive integers.

c. find the length of the rope
d. find the mass of the rope
e. what is the harmonic number of the 4m standing wave?

Homework Equations

f=1/T
T=2pi(m/k)^1/2
=2pi(L/g)^1/2
v=(wavelength)f
F(t)=u(v)^2
f=v/wavelength
2L/n=4m
2L/(n+1)=3.2m

The Attempt at a Solution

a. (0.4 kg/m)(12m/s)^2= 58N

b. f = (12m/s)/(2m) = 6 Hz

c. n=4

2L = 16 for both
L=8m

 

[grzz]

... u, is 0.6kg/m, ... with a wave length of 4m

... The attempt at a solution[/b]

a. (0.4 kg/m)(12m/s)^2= 58N...

u = 0.6kg/m or 0.4kg/m?

 

[somesmallkid]

u = 0.6kg/m or 0.4kg/m?

Oh, it's 0.6kg/m. Sorry it's kind of late and I guess I'm just tired of trying to solve this problem :I hehe..

 

[grzz]

... a traveling wave with a wave length of 4m
b. f = (12m/s)/(2m) = 6 Hz ...

Is not the wavelength 4m?

 

[somesmallkid]

Is not the wavelength 4m?

No, you're right. It's 4.

 

[somesmallkid]

Am I doing these correctly?

 

[grzz]

Length of rope = 8m

 

[somesmallkid]

Length of rope = 8m

yeah i got that :) thanks! do you know how to do D or E though?

 

[grzz]

re D
Your post says,'...The linear density of the rope, u, is 0.6kg/m,...' and you know the length of rope.

re E

What do you understand by 'fundamental frequency'?