16.3 Wave Speed on a Stretched String

The wave speed of a wave on a string depends on the tension and the linear mass density. If the tension is doubled, what happens to the speed of the waves on the string?

If the tension in a string were increased by a factor of four, by what factor would the wave speed of a wave on the string increase?

Guitars have strings of different linear mass density. If the lowest density string and the highest density string are under the same tension, which string would support waves with the higher wave speed?

Electrical power lines connected by two utility poles are sometimes heard to hum when driven into oscillation by the wind. The speed of the waves on the power lines depend on the tension. What provides the tension in the power lines?

A copper wire has a density of $\rho = 8920 \text{kg}/\text{m}^{3} ,$ a radius of 1.20 mm, and a length L. The wire is held under a tension of 10.00 N. Transverse waves are sent down the wire. (a) What is the linear mass density of the wire? (b) What is the speed of the waves through the wire?

A string with a linear mass density of $\mu = 0.0060 \text{kg}/\text{m}$ is tied to the ceiling. A 20-kg mass is tied to the free end of the string. The string is plucked, sending a pulse down the string. Estimate the speed of the pulse as it moves down the string.

A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?

Two strings are attached to poles, however the first string is twice the linear mass density mu of the second. If both strings have the same tension, what is the ratio of the speed of the pulse of the wave from the first string to the second string?

The note $E_{4}$ is played on a piano and has a frequency of $f = 393.88 .$ If the linear mass density of this string of the piano is $\mu = 0.012 \text{kg}/\text{m}$ and the string is under a tension of 1000.00 N, what is the speed of the wave on the string and the wavelength of the wave?

A sinusoidal wave travels down a taut, horizontal string with a linear mass density of $\mu = 0.060 \text{kg}/\text{m}$. The maximum vertical speed of the wave is $v_{y \text{max}} = 0.30 \text{cm}/\text{s} .$ The wave is modeled with the wave equation $y \left(x , t\right) = A \text{sin} \left(6.00 \text{m}^{−1} x - 24.00 \text{s}^{−1} t\right) .$ (a) What is the amplitude of the wave? (b) What is the tension in the string?