第16章波動

Transverse waves are sent along a 5.00-m-long string with a speed of 30.00 m/s. The string is under a tension of 10.00 N. What is the mass of the string?

A copper wire has a density of $\rho =8920{\text{kg/m}}^3,$ 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 piano wire has a linear mass density of $\mu =4.95\times {10}^{\mathrm{-3}}\text{kg/m}.$ Under what tension must the string be kept to produce waves with a wave speed of 500.00 m/s?

A string with a linear mass density of $\mu =0.0060\text{kg/m}$ 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 cord has a linear mass density of $\mu =0.0075\text{kg/m}$ and a length of three meters. The cord is plucked and it takes 0.20 s for the pulse to reach the end of the string. What is the tension of 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 as long as the second. If both strings have the same tension and mu, what is the ratio of the speed of the pulse of the wave from the first string to the second 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?

Transverse waves travel through a string where the tension equals 7.00 N with a speed of 20.00 m/s. What tension would be required for a wave speed of 25.00 m/s?

Two strings are attached between two poles separated by a distance of 2.00 m as shown below, both under the same tension of 600.00 N. String 1 has a linear density of ${\mu }_1=0.0025\text{kg/m}$ and string 2 has a linear mass density of ${\mu }_2=0.0035\text{kg/m}.$ Transverse wave pulses are generated simultaneously at opposite ends of the strings. How much time passes before the pulses pass one another?

Two strings are attached between two poles separated by a distance of 2.00 meters as shown in the preceding figure, both strings have a linear density of ${\mu }_1=0.0025\text{kg/m},$ the tension in string 1 is 600.00 N and the tension in string 2 is 700.00 N. Transverse wave pulses are generated simultaneously at opposite ends of the strings. How much time passes before the pulses pass one another?

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 $\mu =0.012\text{kg/m}$ 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?

Two transverse waves travel through a taut string. The speed of each wave is $v=30.00\text{m/s}.$ A plot of the vertical position as a function of the horizontal position is shown below for the time $t=0.00\text{s}.$ (a) What is the wavelength of each wave? (b) What is the frequency of each wave? (c) What is the maximum vertical speed of each string?

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

The speed of a transverse wave on a string is $v=60.00\text{m/s}$ and the tension in the string is $F_T=100.00\text{N}$. What must the tension be to increase the speed of the wave to $v=120.00\text{m/s?}$