The light’s wavelength is
6.0×10í^7 m. The light completes
5.0 cycles in 10í^14 seconds. What
is the light’s wave speed?
v = Ȝf
v = (6.0×10í^7 m)(5.0×10^14 Hz)
v = 3.0×10^8 m/s
15.8 - Wave speed in a string
This section examines in detail the physical factors that determine the speed of a
transverse wave in a string. The factors are the force on the string (the string’s tension)
and the string’s linear density. Linear density is the mass per unit length, m/L. It is
represented with the Greek letter μ (pronounced “mew”).
The relationship of wave speed to the string’s tension and linear density is expressed in
Equation 1. The equation states that the wave speed equals the square root of the
string tension divided by the linear density of the string.
Your physics intuition may help you understand why wave speed increases with string
tension and decreases with string density.
Consider Newton’s second law, F= ma. If the mass of a particle is fixed, a larger force
on the particle will result in a greater acceleration. When a string under tension is
shaken up and down, the tension acts as a restoring force on the string, pulling its
particles back toward their rest positions. The greater the tension, the greater this
restoring force and the faster the string will return to equilibrium. This means the string
will oscillate faster (its frequency increases). Because wave speed is proportional to
frequency, the speed will increase with the tension.Now let’s assume that the tension is fixed, and compare wave speeds in strings that
have differing linear densities (mass per unit length). Newton’s second law says that for
a given restoring force (tension), the particles in the more massive string will have less
acceleration and move back to their rest positions more slowly. The wave frequency
and wave speed will be less.
The equation on the right is a good approximation when the amplitude of the wave is
significantly smaller than the overall length of the medium though which the wave
moves. The force that causes the wave must also be significantly less than the tension
for this equation to be accurate. The equation can be derived using the principles
discussed in this section.Wave speed in a string
Increases with string’s tension
Decreases with string’s linear densityv = wave speed
F = string tension
m = string mass
L = string length
(^300) Copyright 2007 Kinetic Books Co. Chapter 15