Calculate Tension in Transverse Wave on String: Linear Density 1.87x10-2kg/m

[wesochick6]

A transverse wave is traveling on a string. The displacement y of a particle from its equilibrium position is given by y = (0.0221 m) sin (28.9t - 2.20x). Note that the phase angle 28.9t - 2.20x is in radians, t is in seconds, and x is in meters. The linear density of the string is 1.87 x 10-2 kg/m. What is the tension in the string?

I;m just not sure how density factors into any of this, I'm not sure i need help to solve the problem, just an equation which relates density to waves.

 

[chaoseverlasting]

Hi, welcome to PF. From the equation given to you, you have the wave number and the angular frequency. From these two quantities, you can find the velocity of the wave. Velocity of a wave on a string is related to the tension of the string. Do you know these relations?

 

[bizonek]

I think an essential formula here is:
v=sqrt(F/d)
where: v-velocity of a wave, d-linerar density of the string and F is of course the tension of string.

heh... It's my firs post on this forum. :)

 

[chaoseverlasting]

Yeah, that's one of them. Now you need the one for wave number - velocity.

 

[bizonek]

From the second part of the equation which was given we can calculate:
2*pi*f=28,9
2*pi/l=2,20
where f-frequency of the wave, l-lenght of the wave, pi is 3,1415... (how can I write formulas, equations in a 'nice' way?)

then we need to use:
v=l*f
and we can calculate velocity of the wave.
Of course, we used the relevant units.

 

[wesochick6]

Thanks so much i am going to try to work through it and see how it goes... hopefull better than before