Lesson: Propagation of Waves along a String

Learn to model the propagation of waves along strings of particular linear mass densities and tensions.

Worksheet: Propagation of Waves along a String • 9 Questions

Q1:

A string with a linear mass density of 0.0060 kg/m is tied to the ceiling and a mass of 20 kg is tied to the free end of the string. The string is plucked, sending a pulse down the string. Find the speed of the pulse down the string.

Q2:

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?

Q3:

Two strings, both with a tension of 600 N, are attached between two vertical poles separated by a horizontal distance of 2.00 m. String one has a linear mass density and string two has a linear mass density . Transverse wave pulses and are generated simultaneously at opposite ends of the strings, moving at speeds and respectively. How much time after the wave pulses are produced do both pulses’ leading edges intersect a line that is parallel to both poles?

Q4:

A transverse wave on a horizontal string with linear mass density of 0.00600 kg/m is described with the equation

where is the wave’s angular frequency, is measured in meters, and is measured in seconds.

The string is under a tension of N.

At what speed does the wave propagate along the string?

What is the wave number of the wave?

What is the angular frequency of the wave?

Q5:

A copper wire has a density of 8 920 kg/m³, a radius of 1.200 mm, and a length . The wire is held under a tension of 10.0 N. Transverse waves are sent down the wire.

What is the linear mass density of the wire?

What is the speed of the waves through the wire?

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