3.3 Waves
3.3.1 Progressive and Stationary Waves
3.1.1.1 Progressive Waves
● Oscillation of particles of the medium
● Amplitude - maximum displacement of point on a wave
● Wavelength - distance from a point on one wave to equivalent point on
adjacent wave
● Frequency - number of waves passing a point each second
● Frequency = 1/time period
● f = 1/T
○ T is time period in seconds (s)
○ f is frequency in hertz (Hz)
● Wave speed - speed at which energy is transferred (or wave moves)
through medium
● Wave Equation:
○ V= fλ
○ V= velocity (m/s) → also noted as c
○ f= frequency (Hz)
○ λ= wavelength (m)
○ f= V/λ
○ λ= V/f
Phase Difference
● Phase is the proportion of a complete wave an individual place in the wave
has completed since the start of the cycle
● Phase difference is a way of describing how far apart 2 waves are in their
respective cycles
● In phase → 2 points on different waves are in the same phase of their wave
● Out of phase → 2 points on different waves are in slightly different phases
of their wave
● Completely out of phase → a peak in one wave is at the point of a trough in
another
, Radians
● 2 r = circumference
● r = ½ circle arc length
● Length around circle = angle x radius
● E.G 360° = 2 rad, 180° = rad, etc.
Phase as Fractions
● Waves in phase are both at same point in their cycle at the same time
● Waves in phase will produce a standing wave
● ¼ wave = peak to equilibrium, ½ wave = peak to trough, 1 wave =
peak-trough-peak
Phase as Angles
● Phase difference described in terms of degrees or radians
● E.G ½ cycle behind = 180° = rad, ¼ behind = 90° = /2 rad
● Written as ‘phase of 180°’ or ‘delayed by 180°’
Finding Phase Difference
● Find distance between 2 corresponding points (e.g 2 peaks) - ‘d’
● Divide by wavelength of wave
● Then multiply by 360 to get degrees or multiply by to get radians
2 d 360d
P hase Dif f erence = λ or λ
3.1.1.2 Longitudinal and Transverse Waves
Longitudinal Waves
Vibrations are parallel to the direction of energy transfer
3.3.1 Progressive and Stationary Waves
3.1.1.1 Progressive Waves
● Oscillation of particles of the medium
● Amplitude - maximum displacement of point on a wave
● Wavelength - distance from a point on one wave to equivalent point on
adjacent wave
● Frequency - number of waves passing a point each second
● Frequency = 1/time period
● f = 1/T
○ T is time period in seconds (s)
○ f is frequency in hertz (Hz)
● Wave speed - speed at which energy is transferred (or wave moves)
through medium
● Wave Equation:
○ V= fλ
○ V= velocity (m/s) → also noted as c
○ f= frequency (Hz)
○ λ= wavelength (m)
○ f= V/λ
○ λ= V/f
Phase Difference
● Phase is the proportion of a complete wave an individual place in the wave
has completed since the start of the cycle
● Phase difference is a way of describing how far apart 2 waves are in their
respective cycles
● In phase → 2 points on different waves are in the same phase of their wave
● Out of phase → 2 points on different waves are in slightly different phases
of their wave
● Completely out of phase → a peak in one wave is at the point of a trough in
another
, Radians
● 2 r = circumference
● r = ½ circle arc length
● Length around circle = angle x radius
● E.G 360° = 2 rad, 180° = rad, etc.
Phase as Fractions
● Waves in phase are both at same point in their cycle at the same time
● Waves in phase will produce a standing wave
● ¼ wave = peak to equilibrium, ½ wave = peak to trough, 1 wave =
peak-trough-peak
Phase as Angles
● Phase difference described in terms of degrees or radians
● E.G ½ cycle behind = 180° = rad, ¼ behind = 90° = /2 rad
● Written as ‘phase of 180°’ or ‘delayed by 180°’
Finding Phase Difference
● Find distance between 2 corresponding points (e.g 2 peaks) - ‘d’
● Divide by wavelength of wave
● Then multiply by 360 to get degrees or multiply by to get radians
2 d 360d
P hase Dif f erence = λ or λ
3.1.1.2 Longitudinal and Transverse Waves
Longitudinal Waves
Vibrations are parallel to the direction of energy transfer
