CK- 12 Refraction of Mechanical Waves
The refraction of waves across
boundaries operates similarly to the
method by which tanks are steered.
Tanks do not have a steering wheel.
Instead, they have an accelerator to
produce forward motion and
separate brakes on each tread. The
operator uses brakes on both treads at the same time in order
to stop, but brakes on only one tread to turn the tank. By
braking one side, the operator causes that side to slow down or
stop while the other side continues at the previous speed,
causing the tank to turn towards the slower tread.
This sketch above shows a wave ray
striking an interface between an old medium
and a new medium. A normal line has been
drawn as a dotted line perpendicular to the
interface. The angle between the incident
ray and the normal line is called the angle of
incidence, shown as θi, and the angle between the refracted
ray and the normal line is called the angle of refraction, θr.
We already understand that the change in the wave
direction at the border depends on the difference between the
two velocities. This relationship is conveniently expressed in a
mathematical relationship:
Refraction of Mechanical Waves
When any wave strikes a boundary
between media, some of the energy is
reflected and some is transmitted. When the
wave strikes the media interface at an angle,
the transmitted wave will move in a slightly
different direction than the incident wave.
This phenomenon is known as refraction.
Consider the image sketched above. Suppose that the
waves represented here are water waves. The wave crests are
represented by the black lines in the image. As such, the
distance between two consecutive black lines is the
wavelength. Let the red line represent a transition from deep to
shallow water. This transition is called the media interface. As
the waves hit the boundary, the waves slow down. The right
side of the wave reaches the boundary before the left side of
the wave, causing the left side to catch up and the angle of
propagation to change slightly. This change in direction can be
seen in the yellow line, which is slightly angled at the boundary.
The ratio of the sine of the angle of refraction to the sine
of the angle of incidence is the same as the ratio of the velocity
of the wave in the new medium to the velocity of the wave in
the old medium and equal to the ratio of wavelength (λ) in the
old medium to the wavelength in the new medium.
Questions
1. What causes refraction?
2. What doesn’t change during refraction?