string of length L is under tension, and the speed of a wave in the string is 58 m/s.  What will be the speed of a wave in the string, in m/s, if the length is doubled but with no change in the mass or tension?

A stationary boat in the ocean is experiencing waves from a storm. The waves move at 56 km/h and have a wavelength of 160 m, both typical values. The boat is at the crest of a wave. How much time elapses until the boat is first at the trough of a wave?

A Slinky stretched to 4.00 m carries a wave along its length. (a) How fast does the wave propagate if it takes 2.4 s to travel down the Slinky and back again? (b) In the same Slinky, a standing wave with four nodes and three antinodes is set vibrating. What is the frequency of vibrations?

A mass M = 2.3 kg is hanging from a long string of length L = 21.5 m and total mass m = 16 kg. A student gives the mass a quick horizontal shake to set up a wave which travels upwards along the string. Express the tension of the chain at a height y above the bottom in terms of M, m, and g.  What is the speed of the wave, in meters per second, at the top of the string?   How long does it take, in seconds, for the wave to travel up the string?

Transverse waves on a string have a wave speed of 8.00 m / s, an amplitude of 0.070 m and a wavelength of 0.320 m.These waves travel in the +x direction, and at t = 0 the end x = 0 of the chord is at y = 0 and is moving downward. (a) Find the frequency, period and wave number k= 2/λ of these waves. (b) Write the equation for y (x, t) describing these waves. (c) Find the transverse displacement of a point on the chord at x = 0: 360m at time t = 0: 150s. (Show the formulas with explanations and steps please)

Two children stretch a jump rope between them and send wave pulses back and forth on it. The rope is 4.5 m long, its mass is 0.64 kg, and the force exerted on it by the children is 47 N. (a) What is the linear mass density of the rope (in kg/m)? kg/m (b) What is the speed of the waves on the rope (in m/s)? m/s

Oscillation of a 600 Hz tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is 400 m/s. The standing wave has four loops and an amplitude of 2.0 mm. (a) What is the length of the string? (b) Write an equation for the displacement of the string as a function of position and time.

A 120-cm string has a total mass of 80 g.  One end of the string is tied to a post.  A pulley is placed 90 cm from the post, and a mass of 265 g is suspended from the other end of the string, and hung over the pulley.  (a) What do you expect the speed of waves on the string to be equal to?  (b)  What is the frequency of a standing wave on this string which has four antinodes?

Two children stretch a jump rope between them and send wave pulses back and forth on it. The rope is 4.7 m long, its mass is 0.40 kg, and the force exerted on it by the children is 31 N. (a) What is the linear mass density of the rope (in kg/m)?   kg/m (b) What is the speed of the waves on the rope (in m/s)?   m/s

Transverse waves with a speed of 46.5 m/s are to be produced on a stretched string. A 5.40-m length of string with a total mass of 0.0600 kg is used. (a) What is the required tension in the string? (b) Calculate the wave speed in the string if the tension is 8.00 N. m/s