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Reflection and Refraction of Waves

When sound waves are incident on a boundary between two media, a part of incident waves returns back into the initial medium (reflection) while the remaining is partly absorbed and partly transmitted into the second medium (refraction) (Fig. 1).
Fig. 1
  • The frequency of the wave remains unchanged that means ωi = ωr = ωt = ω = constant
  • The incident ray, reflected ray, normal, and refracted ray all lie in the same plane.
  • For reflection, angle of incidence (i) = angle of reflection (r).
  • For refraction, 32310.png
  • In reflection from a denser medium or rigid support, phase changes by 180° and direction reverses. If incident wave is y = A1 sin (ω tkx), then reflected wave becomes y = Ar sin (ω t + kx + π) = –Ar sin (ωt + kx).
  • In reflection from a rarer medium or free end, phase does not change and direction reverses if incident wave is y = AI sin (ωtkx) then reflected wave becomes y = Ar sin (ωt + kx)
    Fig. 2
  • Echo is an example of reflection.
    If there is a sound reflector at a distance d from the source, then time interval between original sound and its echo at the site of source will be t = 2d/v.
Table 1 Reflection of Mechanical Waves


Longitudinal wave

Transverse wave

Change in direction

Phase change

Path change

Compression as rarefaction and vice-versa

Crest as crest and trough as trough




Reflection from free end/rarer medium

Compression as compression and rarefaction as rarefaction

Crest as trough and trough as crest

No change



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