Question

Given Tension and the wave equation, how do you find the linear density?

Answer 1

I am given that the equation of a transverse wave of a string is y(x,t) = 2.00mm(sin(25.1rad/m)x-(415 rad/s)t) and the string is under 18 N of tension. From the tension, I got that the string is roughly 1.84 kg using F = ma. I know that the speed of a the string is equal to the root of the tension over the linear density, but how do I find the linear density. Am I supposed to derive the wave equation? But if I am, I am a bit confused as to with respect to what variable dx or dt and why. Even then, when I derive the equation will I still be getting velocity, as the function is not x(t), which when derived would give me v(t).

Answer 2

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✔️✔️Given Tension and the wave equation, you find the linear density


y(x,t) = 2.00mm(sin(25.1rad/m)x-(415 rad/s)t) and the string is under 18 N of tension.

From the tension, I got that the string is roughly 1.84 kg using F = ma.

I know that the speed of a the string is equal to the root of the tension over the linear density, but how do I find the linear density.

Am I supposed to derive the wave equation?

But if I am, I am a bit confused as to with respect to what variable dx or dt and why.

Even then, when I derive the equation will I still be getting velocity, as the function is not x(t), which when derived would give me v(t).


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