18. Waves & Sound

Velocity of Transverse Waves

Multiple Choice
A 2 m long string is arranged as shown in the figure below. If the mass of the string is 0.5 kg, what would the frequency be of a wave with a 2 cm wavelength?
Multiple Choice
A rope with length 2.50 m and mass 0.10 kg is stretched and pulled to create transverse waves of frequency 40.0 Hz and wavelength of 0.750 m. How much tension is exerted on the rope?
Multiple Choice
An oscillating blade creates waves on a string. If the amplitude of the wave doubles, what happens to the wavelength λ and v?
Open Question
The string in FIGURE P16.59 has linear density μ. Find an expression in terms of M, μ, and θ for the speed of waves on the string.
Open Question
FIGURE P16.57 shows a snapshot graph of a wave traveling to the right along a string at 45 m/s. At this instant, what is the velocity of points 1, 2, and 3 on the string?
Open Question
String 1 in FIGURE P16.47 has linear density 2.0 g/m and string 2 has linear density . A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. What should the string lengths L₁ and L₂ be if the pulses are to reach the ends of the strings simultaneously?
Open Question
A string that is under 50.0 N of tension has linear density 5.0 g/m. A sinusoidal wave with amplitude 3.0 cm and wavelength 2.0 m travels along the string. What is the maximum speed of a particle on the string?
Open Question
The wave speed on a string under tension is 200 m/s. What is the speed if the tension is halved?
Open Question
(II) A 0.40-kg cord is stretched between two supports 8.7 m apart. When one support is struck by a hammer, a transverse wave travels down the cord and reaches the other support in 0.85 s. What is the tension in the cord?
Open Question
(II) A 4.4-kg ball hangs from a steel wire 1.00 mm in diameter and 5.00 m long. What would be the speed of a transverse wave in the steel wire?
Open Question
(II) A ski gondola [pronounced gon–do–la] is connected to the top of a hill by a steel cable of length 710 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a transverse wave pulse along the cable. It is observed that it took 17 s for the pulse to return.
(b) What is the tension in the cable?
Open Question
(I) A transverse wave on a wire is given by D (x, t) = 0.015 sin ( 35x - 1200 t) where D and x are in meters and t is in seconds.
(b) What is the speed of either wave?
Open Question
A 10.0-m-long wire of mass 138 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?
Open Question
A uniform cable 2.0-m long hangs vertically under its own weight.

(a) Determine the speed of waves on the cable as a function the distance y (positive down from the top of the cable, where y = 0 ).