As in Figure P18.16, a simple harmonic oscillator is attached to a rope of linear mass density 5.4 102 kg/m, creating a standing transverse wave. There is a 3.6-kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 43.2 rad/s and an amplitude of 24.6 cm. a. What is the distance between adjacent nodes? b. If the angular frequency of the oscillator doubles, what happens to the distance between adjacent nodes? c. If the mass of the block is doubled instead, what happens to the distance between adjacent nodes? d. If the amplitude of the oscillator is doubled, what happens to the distance between adjacent nodes? FIGURE P18.16

At t = 0, a transverse pulse in a wire is described by the function y=6.00x2+3.00 where xand y are in meters. If the pulse is traveling in the positive x direction with a speed of 4.50 m/s, write the function y(x, t) that describes this pulse.

A steel wire of length 30.0 m and a copper wire of length 20.0 m, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 150 N. During what time interval will a transverse wave travel the entire length of the two wires?

The equation of a harmonic wave propagating along a stretched string is represented by y(x, t) = 4.0 sin (1.5x 45t), where x and y are in meters and the time t is in seconds. a. In what direction is the wave propagating? be. N What are the b. amplitude, c. wavelength, d. frequency, and e. propagation speed of the wave?

Review. A sphere of mass M = 1.00 kg is supported by a string that passes over a pulley at the end of a horizontal rod of length L = 0.300 m (Fig. P17.15). The string makes an angle = 35.0 with the rod. The fundamental frequency of standing waves in the portion of the string above the rod is f = 60.0 Hz. Find the mass of the portion of the string above the rod. Figure P17.15 Problems 15 and 16.

Review. A sphere of mass M is supported by a string that passes over a pulley at the end of a horizontal rod of length L (Fig. P14.25). The string makes an angle θ with the rod. The fundamental frequency of standing waves in the portion of the string above the rod is f. Find the mass of the portion of the string above the rod. Figure P14.25 Problems 25 and 26.

A tuning fork is known to vibrate with frequency 262 Hz. When it is sounded along with a mandolin siring, four beats are heard every second. Next, a bit of tape is put onto each line of the tuning fork, and the tuning fork now produces five beats per second with the same mandolin siring. What is the frequency of the string? (a) 257 Hz (b) 258 Hz (c) 262 Hz (d) 266 Hz (e) 267 Hz

A copper wire, whose cross-sectional area is 8.58 x 106 m², has a linear density of 6.18 x 103 kg/m and is strung between two walls. At the ambient temperature, a transverse wave travels with a speed of 60.8 m/s on this wire. The coefficient of linear expansion for copper is 17 x 10-6 (Cº)-1, and Young's modulus for copper is 1.1 x 10¹1 N/m². What will be the speed of the wave when the temperature is lowered by 26.5 Cº? Ignore any change in the linear density caused by the change in temperature. Number i Units

An aluminum rod, 1.00 m long, is held lightly in the middle. One end is struck head-on with a rubber mallet so that a longitudinal pulse—a sound wave—travels down the rod. The fundamental frequency of the longitudinal vibration is 1.10 kHz. Calculate the speed of sound in aluminum from the information given in the problem.