When a wave meets a boundary, part of it can reflect (bounce back into the same medium) and part can refract (change direction as it enters a new medium). Drawing wavefronts lets you see why.
This lesson belongs to wave behaviour. It uses the wave equation from connecting wavelength, frequency and speed.
What is a wavefront and why does it help?
A wavefront is a line joining points that are at the same stage of the wave, such as all the crests at one moment. Rays are drawn at 90° to the wavefronts, showing the direction of travel.
Ripple-tank pictures show wavefronts as parallel lines. Because they show wavelength as the gap between lines, they let you compare waves before and after a boundary.
What happens in reflection?
The wave stays in the same medium, so its speed, frequency and wavelength are unchanged. Only the direction changes. The angle of incidence equals the angle of reflection, both measured from the normal.
The angle between a wavefront and the reflecting surface equals the angle between the ray and the normal. So you can read the angle of incidence from wavefronts directly.
What happens in refraction?
A wave entering a new medium changes speed. The frequency stays the same because it is set by the source. From v = f × λ, a change in speed therefore means a change in wavelength.
The direction changes because the wavefront does not enter all at once. The end that meets the new medium first changes speed first, so the front pivots. A slower wave has its wavefronts closer together and bends towards the normal.
Worked example
Invented data: ripples of frequency 4.0 Hz and wavelength 0.060 m move from deep water into a shallow region, where their speed falls to 0.16 m/s. Find the new wavelength and describe the change in direction.
Step 1, speed in deep water: v = f × λ = 4.0 × 0.060 = 0.24 m/s.
Step 2, frequency in shallow water: unchanged at 4.0 Hz.
Step 3, new wavelength: λ = v ÷ f = 0.16 ÷ 4.0 = 0.040 m.
Step 4, direction: the waves slow down, so the wavefronts bunch closer and the ray bends towards the normal (unless it arrived along the normal, in which case it does not bend).
Check: 4.0 × 0.040 = 0.16 m/s, which matches the speed given.
The mistake to watch for
A common error is to say that the frequency decreases when a wave slows down.
Mistaken answer: “The wave slows, so its frequency decreases and the wavelength stays the same.”
This reverses the roles. The frequency is fixed by the source, and the wavelength shortens.
The correction has two parts. State the quantity that is unchanged first (frequency), then use v = f × λ to show what must change.
The second common slip is measuring an angle to the surface instead of to the normal. The triangle and bearings reasoning board gives practice at choosing the right angle before calculating.
Check yourself
1. Waves of frequency 5.0 Hz slow from 0.30 m/s to 0.20 m/s at a boundary. Find the new wavelength.
Show answer
Frequency stays at 5.0 Hz. λ = 0.20 ÷ 5.0 = 0.040 m.
2. A plane wavefront meets a straight barrier, making an angle of 30° with it. What is the angle of reflection?
Show answer
The angle between wavefront and barrier equals the angle between ray and normal, so the angle of incidence is 30°. The angle of reflection is also 30°.
3. Waves move from shallow water into deeper water. State the change in wavelength and in direction.
Show answer
The waves speed up, so the wavelength increases (frequency is unchanged). They bend away from the normal.
Where this leads next
Reflection and refraction apply to all waves, not only ripples. To see how wave motion differs between sound and water, read transverse and longitudinal motion. Light is developed further in light and imaging.
Explanations like these are easiest to improve when a teacher reads them with you. That is a natural use of online one-to-one Physics tuition.