# PHYS 2211 Module 14.3

## Wave Speed on a Stretched String

14.3 Wave Speed on a Stretched String

### Learning Objectives

By the end of this section, you will be able to:

• Determine the factors that affect the speed of a wave on a string
• Write a mathematical expression for the speed of a wave on a string and generalize these concepts for other media

### Wave Speed on a String under Tension

Practice!

The physical factors that affect the speed of a wave traveling in a string are both the tension force in the string and the mass density of the string. The speed of a wave in a string depends on the magnitude of the tension, FT, in the string and the mass density, µ, of the string. The speed of the wave can be calculated with .

If you replaced the hanging block with one that is twice as heavy, the speed of the wave would increase by a factor of . The speed of a wave in a string depends on the magnitude of the tension, FT, in the string and the mass density, µ, of the string. The speed of the wave can be calculated with . If you hang a block from the string that is twice as heavy, the tension in the string will double in magnitude. The calculation for the new wave speed using the heavier block is , which is faster than the original speed by a factor of .

If you replaced the string with one that has two times the mass density, the speed of the wave would decrease by a factor of . The speed of a wave in a string depends on the magnitude of the tension, FT, in the string and the mass density, µ, of the string. The speed of the wave can be calculated with . If you use a string that has twice the mass density of the original string, then the mass density becomes 2µ. The calculation for the new wave speed using the heavier string is , which is slower than the original speed by a factor of .

Discuss!

A heavy uniform rope hangs from the ceiling, and a small amplitude transverse wave is started by jiggling the rope at the bottom. As the wave travels up the rope, will the wave speed increase, decrease, or remain constant?

Three waves are traveling along identical strings. Wave B has twice the amplitude of the other two. Wave C has 1/2 the wavelength than A or B.

(a) Which wave goes fastest?

(b) Which wave, A or C, has the higher frequency?