phy C2 wave model

waves

• caused by disturbances which result in oscillations that are spread out as waves

  • travelling waves: particles of medium oscillate about equilibrium position → transmit disturbance to other particles BUT particles do not move along with disturbance

  • as disturbance moves through the medium, wave is propagated and energy is transported

• continuous wave produced when medium is disturbed in a regular, periodic way. repeats itself.

• wave pulse produced when medium is disturbed briefly. wave pulse is an isolated disturbance that travels through an otherwise undisturbed medium.

travelling/progressive waves

• movement of a disturbance from a source that transfers energy but not material to places around it

• examples

  • mechanical waves (require a medium for propagation)

  • EM waves (do not require a medium)

• types: transverse/longitudinal

transverse waves

• displacement of particles is perpendicular to direction of wave propagation/energy transfer

• eg EM waves

longitudinal waves

• displacement of particles in the medium is perpendicular to direction of wave propagation/energy transfer

• series of compressions/rarefactions

  • at centre of compression/rarefaction, displacement = 0

  • consider if moved left/right when plotting displacement-distance graph

• eg sound waves

wavelength

distance between any two successive points in phase

period

time taken for particle to undergo one complete cycle of oscillation/time taken for wave to travel through one wavelength

frequency

no. of complete cycles performed by a particle per unit time/no. of wavelengths that pass a given point per unit time

wave speed

• distance the wave profile moves per unit time

  • NOT the speed of oscillating particles!

• derivation (to memorise)

  • speed = distance/time

  • distance = 1 wavelength λ, time = period T

  • v = λ/T = fλ

how to find wavelength?

• displacement-distance graph

  • how displacements of particles vary with distance from source at a fixed moment in time

  • measure distance between successive crests/troughs

how to find period?

• displacement-time graph

  • how displacement of a single particle varies with time

  • measure distance betwen successive crests/troughs

sound

• form of energy that is transferred from one point to another as a longitudinal wave

• vibrating object in medium (eg air) causes shifting of layers of air particles, creating series of compressions and rarefactions

direct measuring of speed of sound

1. using measuring tape, observers A/B positioned at distance d apart in open field

2. observer A fires a starting pistol

3. observer B, on seeing the flash, starts the stopwatch. when hears sound, stops stopwatch. record time interval t.

4. v = distance/time

sources of error

• random error due to human reaction time → repeat experiment and take average

• effect of wind on speed of sound in air (doppler effect) → A/B should exchange positions and repeat experiment to cancel effect

EM waves

• oscillating electric charge produces sinusoidally varying electric and magnetic fields oscillating in phase which are perpendicular to each other and to the direction of wave propagation

• transverse waves

• can travel in vacuum

• in vacuum, same speed

• undergo reflection, refraction, interference, diffraction and polarisation

intensity

• rate of energy flow (ie power) per unit cross-sectional area perpendicular to the direction of wave propagation

• I = P/S = E/tS

• E ∝ A² / ⭐️ I ∝ A²

• inverse square law: as distance of observer from point source increases, power received decreases as energy spreads out over larger area

  • I = P/4πr² → I ∝ 1/r²

  • only for sources which emit in all directions (ie point source, like sun)