The linear density of a vibrating string is 1.3 x 10^-4 kg/m3. A transverse wave is propagating on the string and is described by the equation Y = 0.021 sin (x + 30t) where x and y are measured in meters and t in seconds. The tension in the wire?

Explanation

To find the tension in the wire, we can use the formula:

T = μv^2

where T is the tension, μ is the linear density, and v is the wave speed.

First, we need to find the wave speed. We can do this by analyzing the wave equation:

Y = 0.021 sin (x + 30t)

The wave speed is given by the coefficient of t, which is 30 m/s.

Now we can plug in the values:

T = μv^2

= (1.3 x 10^-4 kg/m) x (30 m/s)^2

= 0.12 N

So the tension in the wire is 0.12 N.

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