# Worksheet: Transverse Waves on Strings

In this worksheet, we will practice relating the speed of waves propagating along strings to the dimensions of strings and the tension in them.

**Q1: **

A string on a musical instrument produces waves with a frequency of 128 Hz. Two complete wavelengths of the waves are equal to the length of the string. The mass of the string is 7.5 g.

What is the ratio of the tension in the string to the length of the string?

What is the ratio of the speed of waves on the string to the length of the string?

- A31 s
^{−1} - B93 s
^{−1} - C120 s
^{−1} - D64 s
^{−1} - E16 s
^{−1}

**Q2: **

Suppose that a length of cable could be suspended just above the ground and stretch all the way around the world, requiring a 40,030 km long cable. If the cable has a mass of 1.75 kg per meter of length and if waves travel along the entire length of the cable in exactly one day, what tension would be needed in the cable?

**Q3: **

A thin copper cable and a thin aluminum cable are both oscillated, and waves propagate along them. The waves in the copper cable travel at 33.0 m/s and the waves in the aluminum cable travel at 55.0 m/s. Find the ratio of the tension in the copper cable to the tension in the aluminum cable. Use a value of 0.0149 kg/m for the linear mass density of copper and a value of 0.00472 kg/m for the linear mass density of aluminum.

**Q4: **

A piece of string that is 5.2 m long is held taut at one end by a force of 2.8 N, while the other end of the string is made to oscillate. Waves propagate along the string at 16.6 m/s. What is the mass of the string?

**Q5: **

Which of the following formulas correctly relates the speed of a wave along a string to the mass of the string, the tension in the string, and the length of the string?

- A
- B
- C
- D
- E

**Q6: **

A piece of string that is 3.3 m long has a mass of 115 g. The string is held taut at one end by a force of 25 N. When the other end of the string is made to oscillate, waves propagate along the string. At what speed do waves propagate along the string?

**Q7: **

A string on a musical instrument produces waves with a frequency of 256 Hz. Four complete wavelengths of the waves are equal to the length of the string. The mass of the string is 5.5 g and it has a tension of 16 N.

At what speed do waves propagate along the string?

What is the wavelength of the waves on the string?

What is the ratio of the wavelength of the sound waves in air produced by the string to the wavelength of the waves on the string if the speed of sound in the air near the string is 330 m/s?

**Q8: **

Two strings, string I and string II, have the same length and mass. Waves propagate along both strings, generated by oscillations of the same frequency. The wavelength of the waves propagating along string I is twice the wavelength of the waves propagating along string II. If the tension in string II is 24 N, what is the tension in string I?

**Q9: **

A piece of string that is 1.96 m long has a mass of 65 g. The string is held taut at one end, while the other end of the string is made to oscillate. Waves propagate along the string at 15 m/s. How much force is applied to hold the string taut?

**Q10: **

A metal cable under a tension of 1,100 N has a linear mass density of 0.0095 kg/m. Transverse waves with a frequency of 24 Hz propagate along the cable. How many wavelengths of the waves on the string do the waves propagate through in a time of 3.25 s?

**Q11: **

String I and string II have the same length and the same tension in them. The strings are oscillated simultaneously so that wave pulses propagate along each of them. At a time seconds after the pulses are generated, they have propagated distances and , respectively, along the strings.

Which string has the greater mass?

- AString II
- BString I

Given that , what is the ratio of the mass of the heavier string to the mass of the lighter string?