5.3 - Reflection of Waves

Wavefronts

A wavefront joins points in phase in a wave. These points have the same displacement and are the same distance from the source.
Plane waves have straight, parallel wavefronts; circular waves have circular wavefronts.
The direction of propagation is perpendicular to the wavefront.
The separation of two consecutive wavefronts is one wavelength, $λ$ .
In a ripple tank, crests concentrate transmitted light into bright fringes; troughs spread the light, forming dark fringes.

Water, light and sound waves can undergo reflection. Sea waves reflected by an embankment are an example.
The angle of incidence, $i$ , equals the angle of reflection, $r$ . Both angles are measured from the normal to the reflector.
Reflection changes the direction of propagation; wavelength, frequency and wave speed remain unchanged.
Incident and reflected waves in a ripple tank can be made to appear stationary with the same stroboscope setting, showing that their frequencies are the same.

The incident direction is perpendicular to the incident wavefronts.
The normal is perpendicular to the reflector at the point of incidence.
The reflected direction lies on the other side of the normal, with $r = i$ .
Reflected wavefronts are perpendicular to the reflected direction and have the same spacing as incident wavefronts.

Medical imaging: reflected ultrasonic waves allow examination of a foetus and internal organs.
Satellite reception: a parabolic dish reflects radio waves towards the antenna on its feed horn.
SONAR: a transducer sends ultrasonic waves into water and receives reflections from fish to identify areas containing fish.
Seabed exploration: different rocks produce different reflected sound patterns, allowing the location, depth and structure of seabed regions containing natural gas to be identified.

An echo travels to the reflecting surface and back. For a sea depth $d$ , wave speed $v$ and total travel time $t$ :

2 d = v t, d = \frac{v t}{2}

For ultrasonic waves with $f = 25 kHz$ , $v = 1500 m s^{- 1}$ and a return time of $120 ms$ :

d = \frac{1 500 ( 120 \times 1 0 ^{- 3} )}{2} = 90 m

λ = \frac{v}{f} = \frac{1 500}{25 \times 1 0 ^{3}} = 0.06 m