If a transmission line in a cold climate collects ice, the increased diameter tends to cause vortex formation in a passing wind. The air pressure variations in the vortexes tend to cause the line to oscillate (gallop), especially if the frequency of the variations matches a resonant frequency of the line. In long lines, the resonant frequencies are so close that almost any wind speed can set up a resonant mode vigorous enough to pull down support towers or cause the line to short out with an adjacent line. If a transmission line has a length of 347 m, a linear density of 3.35 kg/m , and a tension of 65.2 MN . What are (a) the frequency of the fundamental mode and (b) the frequency difference between successive modes?

If you set up the seventh harmonic on a string, (a) how many nodes are present, and (b) is there a node, antinode, or some intermediate state at the midpoint? If you next set up the sixth harmonic, (c) is its resonant wavelength longer or shorter than that for the seventh harmonic, and (d) is the resonant frequency higher or lower?

A uniform rope of mass m and length L hangs from a ceiling.(a)Show that the speed of a transverse wave on the rope is a function of y , the distance from the lower end, and is given by $\mathit{v}\mathbf{=}\sqrt{\mathbf{g}\mathbf{y}}$ .(b) Show that the time a transverse wave takes to travel the length of the rope is given by $\mathit{t}\mathbf{=}\mathbf{2}\sqrt{\mathbf{L}\mathbf{/}\mathbf{g}}$ .

In Fig. 16-42, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m .The separation between P and Q is 1.20 m , and the frequency f of the oscillator is fixed at 120 Hz . The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q. A standing wave appears when the mass of the hanging block is 286.1 g or 447.0 g , but not for any intermediate mass. What is the linear density of the string?

A 1.50 m wire has a mass of 8.70 g and is under a tension of 120 N. The wire is held rigidly at both ends and set into oscillation. (a) What is the speed of waves on the wire? What is the wavelength of the waves that produce (b) one-loop and (c) two loop standing waves? What is the frequency of the waves that produce (d) one-loop and (e) two-loop standing waves?

What phase difference between two identical traveling waves, moving in the same direction along a stretched string, results in the combined wave having an amplitude 1.50 times that of the common amplitude of the two combining waves? (a)Express your answer in degrees, (b) Express your answer in radians, and (c) Express your answer in wavelengths.