Velocity of Transverse Waves Practice Problems

Waves travel at 225 m/s on a strained wire. If the tension is adjusted to 1/5 of the initial value, what is the new speed of the waves on the wire?

You set up two wires with different linear mass densities, as shown below. Wire A has a linear mass density of 0.15 kg/m. The linear mass density of wire B is 0.05 kg/m. If two waves are simultaneously sent through the wires and are to arrive simultaneously on the opposite end, calculate the required wire lengths L_A and L_B.

A mass M is used to tension a wire, as shown. The mass per unit length of the wire is µ. If θ = 30 degrees, M = 3.0 kg, and μ = 0.035 kg/m, calculate the speed of waves traveling on the wire.

A boat is tied to the coast by a 0.85 kg rope. The length of the rope is 5.6 m between the lashing points of the coast and the boat. A sudden jerk of the boat due to the ocean waves creates a transverse wave in the rope, which travels along the rope and reaches the lashing point at the coast in 0.95 s. Find the tension in the rope.

Scientists are experimenting with a super strong material. They made a thin thread out of the material and hung a block of 6.2 kg by the thread from the ceiling. The thread has a length of 4.0 m and a diameter of 1.3 mm. If a transverse wave pulse is created in the thread by giving the block a little jerk, find the speed with which the pulse would move along the thread. [Assume that the material has a density of 8900 kg/m³.]

A guitar fretboard is about 0.65 m in length. A guitar learner plucks a string (made of bronze) of the guitar at one of its endpoints. This creates a transverse wave in the string that takes 2.6 × 10^-3 s to bounce off the other end of the string and reach back at the same endpoint. Given that the diameter of the string is 2.6 × 10^-2 cm, calculate the tension in the string.

[Assume that Bronze has a density of 8800 kg/m³.]

A scientist studying waves has generated two waves on two different strings described by Q(x, t) = 0.032 sin (60x - 3000t) and R (x, t) = 0.032 sin (60x + 3000t). All the quantities are in SI units. Find the speeds of the waves.

A 12.0-m-long metal cable used in a construction crane is under a tension of 250 N and has a mass of 140 g. Where will the two pulses first meet if a pulse is generated at one end, and 30.0 ms later, a second pulse is generated at the opposite end?

Determine the wave speed along a hanging chain as a function of the distance y, measured downward from the top where y equals 0. The chain is 4.0 meters long and hangs vertically due to its own weight.

A clothesline tightened between two supports emits a sound of frequency 55 Hz. Determine the period of waves on the clothesline.

How much time will it take for a wave pulse to travel from one tree to the other along a 0.75 kg rope that is tightly stretched between the trees 8.2 m apart, with a tension of 130 N in the rope?