A transverse wave described by

y = (002 m) sin(10 m⁻¹) x + (30 s⁻¹)t]

propagates on a stretched string having a linear mass density of 12 × 10⁻⁴ kg m⁻¹. Find the tension in the string.

A string of linear mass density 05 g cm⁻¹ and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end (figure 15-E4). The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of 20 cm s⁻¹. The pulse is symmetric about its maximum which is located at a distance of 20 cm from the end joined to the ring. (A) Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape. (B) The shape of the string changes periodically with time. Find this time period. (C) What is the tension in the string?

Two wires of different densities but same area of cross section is soldered together at one end and are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.

A travelling wave is produced on a long horizontal string by vibrating and end up and down sinusoidally. The amplitude of vibration is 10 cm and the displacement becomes zero 200 times per second. The linear mass density of the string is 010 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.

A string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160 N m⁻¹ and is stretched by 10 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring?