A travelling wave is produced on a long horizontal string by vibrating and end up and down sinusoidally. The amplitude of vibration is 1 0 cm and the displacement becomes zero 200 times per second. The linear mass density of the string is 0 10 kg m − 1 and it is kept under a tension of 90 N. (A) Find the speed and the wavelength of the wave. (B) Assume that the wave moves in the position x -direction and at t = 0, the end x = 0 is at its positive extreme position. Write the wave equation. (C) Find the velocity and acceleration of the particle at x = 50 cm at time t = 10 ms.

Question

Philoid · Accepted Answer

A. 30 m s⁻¹, 30 cm

The speed will be,

As the displacement becomes zero 200 times per second, the frequency will be, f=100 Hz.

B. y = (10 cm) cos 2π

At, t=0, and x=0 it has maxima.

So, it consists a phase of ∏/2.

The equation becomes,

C. − 54 m s⁻¹, 20 km s⁻²

The velocity of the particle will be,

At x=50cm and t=10ms;

Now, let us calculate the acceleration

At x=50cm and t=10ms;