PHY C14: Wave Motion

We’re covering:

  • Progressive Waves
    • What is wave motion?
    • Components of wave motion
    • Wave equation

Let’s go!


What is Wave Motion?
Propagation of disturbances which carries energy without transferring matter.

What causes Wave Motion?
Vibrations (oscillations).
The energy from these oscillations propagates through waves.


Wave motion can be observed as:

This chapter will deal with progressive waves.


Waves can also be classified into:

Transverse Wavesdirection of vibration is perpendicular to direction of motion
Longitudinal Wavesdirection of vibration is along direction of motion

See here for more.


Examples of Wave Motion:
There are 2 major groups:

MechanicalElectromagnetic
SoundVisible light
Water wavesRadio waves
Strings, SpringsUltraviolet

Components of Wave Motion

ComponentDefinitionNotationUnit
DisplacementRelative distance from vibrating particle to its rest positionym
AmplitudeMaximum displacement of a particleAm
WavelengthDistance between 2 particles vibrating in phaseλm
PeriodTime taken for any particle to complete one oscillationTs
FrequencyNumber of oscillations any particle completes in 1 second
OR
Number of wavelengths that pass through any fixed point in 1 second
f = 1/THz
SpeedDistance travelled by the wave in 1 secondvms-1
Phase Difference
(see below)
Difference between the position of 2 particles in their cyclesφ
  • m
  • s
  • rad
  • cycles

Representing Phase Difference

wave.gif

The red particles are at different points in their cycle at any moment in time.
The motion of each particle can be graphed against time.

2 Red ParticlesPhase DifferenceGraph of each particle’s motion
1st red particle & 2nd red particleThere is a phase difference:
The 2nd ‘lags’ behind the 1st.
Screenshot 2019-05-11 at 12.06.04 PM.png
2nd red particle & 5th red particleThere is no phase difference

They are in phase

Screenshot 2019-05-11 at 12.07.43 PM.png

Calculating Phase Difference:

UnitDefinitionNotationExample
In metresdistance between the 2 particlesxScreenshot 2019-05-11 at 12.32.06 PM.png
In secondstime difference between identical points in the cycles of 2 particlest
OR
(x/λ)T
Screenshot 2019-05-11 at 12.17.47 PM.png
In cyclesFraction of the distance between particles against a complete wavelength

OR

Fraction of the time difference against a complete period
x/λ

OR

t/T
In radiansAngular difference when motion of each particle is mapped onto a circle

1 cycle = 2π rad

(x/λ)2π
OR
(t/T)2π
In degreesAngular difference when motion of each particle is mapped onto a circle 1 cycle = 360°360(x/λ)°
OR
360(t/T)°

Next, we will look at the wave equation describing speed:
v = fλ

How is the wave equation derived?
Wavelength is the distance travelled by a wave in one cycle: λ

Frequency is the number of cycles per second:
f = 1/T

Speed is distance travelled per second:
v = λ/T

Therefore:
v = fλ

*Remember:
Velocity is the SAME in the SAME MEDIUM.
Two water waves might have different f & thus λ, but they will have same v.
Two sound waves in air travel at the same speed: 343 ms-1


⇐ Previous in Physics: Forced Oscillations
⇐ Previous in AS Physics: Strain Energy
⇒ Next in Physics: Energy & Intensity of Waves

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