# Worksheet: Propagation of Waves along a String

In this worksheet, we will practice relating the propagation characteristics of waves along strings with strings' linear mass densities and tensions.

**Q3: **

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

where is the waveβs 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: **

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 pulsesβ leading edges intersect a line that is parallel to both poles?

**Q7: **

A sinusoidal wave travels down a taut, horizontal string with a linear mass density of 0.060 kg/m. The maximum vertical speed of the wave is 0.30 cm/s. The wave is modeled with the wave equation , where is measured in meters and is measured in seconds.

What is the amplitude of the wave?

What is the tension in the string?

**Q8: **

A 20 kg mass rests on a frictionless ramp inclined at , as shown. A string with a linear mass density of 0.025 kg/m is attached to the 20 kg mass. The string passes over a frictionless pulley of negligible mass and is attached to a hanging mass . The system is in static equilibrium. A wave is induced on the string and travels up the ramp.

What is the mass of the hanging mass ?

At what wave speed does the wave travel up the string?

**Q9: **

A string has a mass of 150 g and a length of 3.4 m. One end of the string is fixed to a lab stand and the other is attached to a spring with a spring constant of N/m. The free end of the spring is attached to another lab pole. The tension in the string is maintained by the spring. The lab poles are placed at positions at which the spring has an extension of 2.00 cm. The string is plucked and a pulse travels along the string. What is the propagation speed of the pulse?

**Q22: **

Two strings, string 1 and string 2, are attached between two poles separated by 3.00 meters as shown in the diagram. Both strings have a linear mass density kg/m. The tension in string 1 is 500.0 N and the tension in string 2 is 800.0 N. Transverse wave pulses are generated simultaneously at opposite ends of the strings. How much time passes before both pulses are located at a point that is on a line parallel to both poles?

**Q23: **

A wire of length 1.80 m has a mass of 5.40 g and is under a tension of 145 N. The wire is held rigidly at both ends and set into oscillation.

What is the speed of waves on the wire?

The string is driven into resonance by a frequency that produces a standing wave with a wavelength equal to 0.720 m. What is the frequency used to drive the string into resonance?

**Q25: **

A brass wire has a radius of
150 ΞΌm and a length of
4.0 m. The wire is
placed under a tension of 30 N
and it stretches by a small amount. A pulse travels down the wire after it has been
plucked. Find the propagation speed of the pulse. Assume the temperature does not
change. Use a value of 2.7 g/cm^{3} for the density of brass and use a value of
N/m^{2} for the Youngβs modulus of brass.