Wave Motion
Chapter 16
Mechanical Waves
• Source : disturbance
- disturbance makes medium vibrates (up/dn, side/side)
• Medium (water, air, string,…)
• Mechanical Wave: periodic (sine/cosine) disturbance
traveling through a medium
b/c motion of hand is
sinusoidal, wave is
sinusoidal also
We do not care about
the wave. We care
about medium’s
element displacement
(sine wave ) y(x,t)
Energy Transfer By Wave Motion
• Disturb (drop a stone, speak,…) a medium (water, air,…)
• Disturbance is energy
• Disturbance creates a wave that transfer energy from A to
B
• Medium matter (water, air, string,…) dose not transfer
- elements oscillate around their equilibrium positions

perpendicular to wave propagation: transverse wave

parallel to wave propagation : longitudinal wave
Traveling Wave On Stretched string
y ( x, t )  A sin(kx  t )
A  amplitude  max imum displacement
k  wave No  No waves / length
  angular frequency  No cycles / sec
kx  t : wave phase  900 ( y  A),  900 ( y   A)
2
2
1
k
,
 2f , f 

T
T
General Form of a Traveling Wave
• If a wave does not pass through zero at t=0, it has a phase
shift
y ( x, t )  A sin( kx  t   )
"" traveling right
"" traveling left
  phase cons tan t
• Phase shift has angle unit
• Can be determined from initial
conditions : t=0,x=0
y ( x, t )  A sin (kx  t   ) shifted right
y ( x, t )  A sin (kx  t   ) shifted left
Wave speed and particle speed
• wave
kx  t  cons tan t
dx

k
  0  v 
wave speed
dt
k
• particle
y ( x, t )  A sin( kx  t )
y
u
 A cos(kx  t )
t
a y   2 y ( x, t )
Examples
A traveling wave passes a point of observation. At this point the
time between successive crests is 0.2 sec. Which of the
following is true a) λ=5cm, b) f=5Hz, c) v=5m/sec, d) λ=0.2
cm, e) not enough info
2. One end of string 6m long is moved up and down with SHM at
f=60Hz. The wave reaches the other end of the string in 0.5
sec. Find λ of the wave on the string
3. The wave function of a harmonic wave on a string is
y( x, t )  0.001m sin( 62.8m1  314s 1t )
a) In what direction does this wave move and what is its speed.
b)find λ, f, T of the wave. C) what is the maximum speed of
any string segment
Wave Speed on a Stretched String
v
T

T  Tension in Newtons
  Linear densit (mass / length)
Waves Carry Energy
Waves transport energy through
medium as they propagate
Hand performs work on the end of
string by moving it up and down.
Energy enters the string and propagates
along its length.
Energy and Power of A Traveling Wave
Along a String
•
•
•
•
•
•
Mechanical Wave transports KE and elastic PE(EPE) along string
Continuous energy supply requires a continuous source for waves
Each string element ‘dm’ and length ‘dx’ is provided with KE and
EPE by tension forces
KE depends on the element velocity: velocity is max at y=0,
velocity is zero at y=A
EPE depends on element stretch: stretching is max at y=0, and
zero at y=A
Power Pavg is the rate of energy transmission
Pavg
1
  2 A2 v
2
Chapter16 Assignment
16.5, 7, 9, 11, 20, 30, 39,47, 53, 55
Pavg
1
  2 A2 v
2