Transverse component of tension in a string

[pritamthakur]

Homework Statement

A transverse sinusoidal wave is produced at one end of a long horizontal string by a bar that moves with an amplitude of 1.12 cm. The frequency of motion of bar is 120 Hz . The linear density (m) of string is 117 gm/m . The other end is attached to a mass of 4.68 kg that hangs under gravity. Find the maximum magnitude of transverse component of tension . Also find the maximum power transferred along the string . Take g=10m/s^2

The Attempt at a Solution

The weight of 46.8 N is being balanced by tension. So tension in the string should be 46.8N. We can get the velocity of wave by the formula v=(T/m)^.5 which comes out to be 20m/s. To find the maximum magnitude of transverse component of tension we need the maximum angle made by the string with the horizontal. We can write the wave equation as y=Asin(2(pi)nt) , n is the frequency (120 Hz) . But how to find the angle ? The power transferred by the string is proportional to A^2. But how to find its variation with time ?

 

[anathema]

Thank you for your question. To find the maximum angle made by the string with the horizontal, we can use the equation for the amplitude of the wave, A = A0sin(kx -ωt). In this equation, A0 represents the maximum displacement from equilibrium, which in this case is the amplitude of 1.12 cm. We can solve for the maximum angle by setting A0 equal to the maximum displacement, which is 1.12 cm.

To find the variation of power with time, we can use the equation P = ω^2A^2. In this equation, ω represents the angular frequency, which can be found by multiplying the frequency (120 Hz) by 2π. Therefore, the power transferred along the string will vary with time according to the equation P = (2π120)^2(1.12)^2 = 169340.8 watts.

I hope this helps. Let me know if you have any further questions.