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 string of length 20 cm and linear mass density 040 g cm⁻¹ is fixed at both ends and is kept under a tension of 16 N. A wave pulse is produced at t = 0 near an end as shown in figure (15-E3), which travels towards the other end. (A) When will the string have the shape shown in the figure again? (B) Sketch the shape of the string at a time half of that found in part (A).

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?

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 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.