Wave Motion

1
Wave Motion
2
Wave Types

• Longitudinal
• Motion parallel to energy transport
• Transverse
• Motion perpendicular to energy transport

3
Properties of Waves

• Wavelength
• l, distance between crests
• Frequency
• f, oscillations per second
• Speed
• How quickly the disturbance moves

l
A
Equilibrium
4
CDR Radio

• What is the wavelength of KLOV Radio?

5
Wave Number

• Time dependent wave
• Wave number
• k is to l as w is to T
• Another form

6
Waves on a String

• Wave velocity
• Ex. What is the velocity of a wave pulse on a 1
  mm diameter Copper wire w/ tension of 230 N?
• (rcu 8.92 103 kg/m3)

T Tension m mass/length
7
Sound Waves

• Compression (High Pressure)
• Rarefaction (Low Pressure)
• Frequency Ranges
• Infrasonic lt 20 Hz
• Audible 20 20k Hz
• Ultrasonic gt 20k Hz

8
Superposition Principle

• When 2 or more waves are present, the resulting
  wave is an algebraic sum of all the waves.
• Interference

9
Adding Waves

• At t 0s, the crests of two waves are located at
  the origin. If the first wave has an amplitude
  of 5 cm and wavelength of 2 m and the second wave
  has an amplitude of 2 cm and a wavelength of 0.5
  m, what does the resulting wave look like?

10
Beats

• Periodic variation in intensity with two waves
  close in frequency.

11
Beat Frequency

• One speaker is transmitting a 10 Hz signal and a
  second is transmitting a 11 Hz signal. What beat
  frequency is experienced?

12
Standing Waves

• Two identical waves traveling in opposite
  directions.

• Antinodes - Max Amplitude

• Nodes - Zero Amplitude

13
Harmonic Series

• Have a node at each end of the string.
• Possible wavelengths
• Frequency

14
Waves on a String

• General Form for normal modes

• Nth harmonic

(n1, 2, 3, )
Ex. A 4.0 g wire is stretched to its full length
of 1.75 meters under a tension of 400 N. What
frequency is heard as it vibrates in the wind?
15
Double OpenEnded Pipe

• Air oscillates in and out of the pipes ends.

Air Displacement
Fundamental
2nd Harmonic
(n1, 2, 3, )
3rd Harmonic
16
Single Open Ended Pipe

• Air oscillates in and out of the pipes ends.

Air Displacement
Fundamental
1st Overtone
(n1, 3, 5, )
2nd Overtone
17
Organ Pipe

• Ex. A pipe organ needs to play a low Bb (116.54
  Hz). If a single open ended pipe is used, how
  long should the pipe be?
• What is the frequency of the 2nd overtone for
  this pipe?

18
The Ear

• Mechanical energy is converted into a neural
  signal in the cochea.
• Nerve cells are triggered by the displacement of
  the basilar membrane.

19
Sound Level

• Intensity - Power transmitted per unit area.
• Intensity Level Perceived intensity of sound.
• Measured in decibels (dB)
• 10 times the intensity is perceived as plus 10 dB
• 2 times the intensity is perceived as plus 3 dB
• Threshold of hearing, I0 10-12 W/m2

(Spherical Wave)
20
Fireworks

• 100 m away from an explosion the intensity level
  is 120 dB. What is the intensity level at 500 m?

21
Speed of Sound

• Air
• Bulk modulus (B) - How easy it is to compress a
  volume of air.
• At 20C and sea level v 343 m/s (air)
• Solids
• Youngs modulus (Y) - How easy it is to compress
  a solid.

22
Doppler Effect

• If a source is stationary wave are emitted
  radially outward.

• Wavelength in direction of motion is compressed.

• Therefore, frequency heard is

(vS and vO considered positive when approaching
each other)
23
Doppler Effect

• While standing at a corner, the siren of the
  police car goes from 530 Hz to 470 Hz as it
  passes by. How fast is the car traveling?

Stationary Source
Moving Source
24
Shock Waves

• Supersonic speeds
• Mach Number
• Angle of shock wave

v velocity of sound
vs velocity of the supersonic object
25
Time Dependence

• A moving function has both time and position
  dependence.
• y f(x-vt) (travel to the right)
• y f(xvt) (travel to the left)
• Ex. Haar Wavelet

T 2s
T 0s
0 m
1 m
2 m
-1 m
-2 m
26
Interference

• Remember the Superposition Principle
• Constructive
• Destructive

r1
Effect
1
r2
Source
2
27
Earthquakes

• S waves Transverse
• Shear
• P waves Longitudinal
• Compression