Chapter 16 Waves

Chapter 16
Waves
16-2 Types of Waves
16-3 Transverse and Longitudinal waves
Figure 16-1 shows a transverse wave. the displacement of every
such oscillating string element is perpendicular to the direction of
travel of the wave, as indicated in Fig. 16-1b.This motion is said to
be transverse, and the wave is said to be a transverse wave.
If you push and pull on the piston in simple
harmonic motion, as is being done in Fig. 162, a sinusoidal wave travels along the pipe.
Because the motion of the elements of air is
parallel to the direction of the wave’s travel,
the motion is said to be longitudinal, and the
wave is said to be a longitudinal wave.
16-4 Wavelength and frequency
Imagine a sinusoidal wave like that of Fig. 16-1b traveling in the positive direction of an x axis. As the
wave sweeps through succeeding elements (that is, very short sections) of the string, the elements
oscillate parallel to the y axis. At time t, the displacement y of the element located at position x is
given by
The names of the quantities in Eq. 16-2 are displayed in Fig. 16-3
Amplitude and Phase
The amplitude ym of a wave, such as that in Fig. 16-4 ,
is the magnitude of the maximum displacement of the
elements from their equilibrium positions as the
wave passes through them. (The subscript m stands for
maximum.) Because ym is a magnitude, it is always a positive
quantity
The phase of the wave is the argument kx -ωt of the sine in Eq. 16-2.
Wavelength and Angular wave Number
The wavelength λ of a wave is the distance (parallel to the direction of the wave’s travel) between
repetitions of the shape of the wave (or wave shape).
We call k the angular wave number of the wave; its SI unit is the radian per meter,
or the inverse meter.
We call ω the angular frequency of the wave; its SI unit is the radian per second.
The frequency f of a wave is defined as 1/T and is related to the angular frequency ω by
16-5 The Speed of traveling wave
Figure 16-7 shows two snapshots of the wave of Eq. 16-2, taken a small time interval t apart. The
wave is traveling in the positive direction of x (to the right in Fig. 16-7), the entire wave pattern
moving a distance Δx in that direction during the interval Δt. The ratio Δx/Δt (or, in the differential
limit, dx/dt) is the wave speed v.
The wave speed is
v
dx
dt
16-6 Wave speed on a stretched String
The speed of a wave along a stretched ideal string depends only on the tension and linear density
of the string and not on the frequency of the wave.
Where  is the tension and μ the linear density of the string
The rate of energy transmession
The average power, which is the average rate at which energy of both kinds is
transmitted by the wave, is
Exercise