5.3 Reflection of Waves
Reflection occurs when waves strike an obstacle or barrier and bounce back into the same medium. Learn how wavefronts behave, why wave speed, frequency and wavelength remain unchanged, and how reflection is used in SONAR and medical ultrasound.
Learning Objectives
- Describe wavefronts and their relationship with the direction of wave propagation and wavelength.
- Investigate and explain the characteristics of reflected waves in terms of angle of incidence, angle of reflection, wavelength, frequency, wave speed, and direction of propagation.
- Draw ray diagrams and wavefront diagrams showing the reflection of water waves by a plane reflector.
- Describe daily life applications of reflection for various types of waves.
- Solve numerical problems involving reflection of waves using \(2d = vt\) and \(v = f\lambda\).
Wavefronts and Reflection at a Plane Barrier
See how crests and troughs form bright and dark fringes, and how incident and reflected wavefronts obey \(i = r\) with constant wavelength.
Ripple Tank: Bright and Dark Fringes
Light passing through crests acts like convex lenses and converges to form bright fringes. Light passing through troughs acts like concave lenses and diverges to form dark fringes.
Reflection of Plane Wavefronts
The incident ray and reflected ray make equal angles with the normal. The reflected wavelength is equal to the incident wavelength.
Short Explanation
What is a Wavefront?
A wavefront is a line that joins points that are in phase in a wave. The direction of propagation is always perpendicular to the wavefront, and the distance between two consecutive wavefronts is the wavelength, \(\lambda\).
Law of Reflection
When a wave is reflected by a plane barrier, the angle of incidence equals the angle of reflection: \(i = r\). Both angles are measured from the normal line.
Wave Characteristics During Reflection
Wavelength, frequency and wave speed remain unchanged because the wave stays in the same medium and comes from the same source. Only the direction of propagation changes.
Echo and Depth Calculation
For a reflected pulse, the total distance travelled is twice the distance to the reflector: \(2d = vt\), so \(d = \dfrac{vt}{2}\).
| Wave characteristic | During reflection | Reason |
|---|---|---|
| Angle of incidence and reflection | \(i = r\) | Law of reflection |
| Wavelength, \(\lambda\) | No change | Same medium and same source |
| Frequency, \(f\) | No change | Determined by the source of vibration |
| Wave speed, \(v\) | No change | Same medium, so \(v = f\lambda\) remains constant |
| Direction of propagation | Changes | The wave bounces back with \(i = r\) |
Reflection / Echo Formula
\(2d = vt\)\(d\) = distance to reflecting barrier or depth of sea (m), \(v\) = wave speed (m s⁻¹), \(t\) = total time between transmission and reception (s).
Try to Answer First
Answer in your mind, then press “Check Answer”.
What happens to the wavelength and speed of a water wave when it undergoes reflection?
Check Answer
What is the angle between the wavefront and the direction of wave propagation?
Check Answer
An ultrasonic signal is sent from a ship to the seabed. The echo is received \(0.06\text{ s}\) later. If the speed of sound in water is \(1\,500\text{ m s}^{-1}\), what is the depth of the sea?
Check Answer
Common Mistakes
- Measuring the angle of incidence or reflection from the barrier surface instead of from the normal line.
- Drawing reflected wavefronts with a different spacing compared to the incident wavefronts.
- Drawing wavefronts parallel to the direction of propagation instead of perpendicular (\(90^\circ\)).
- Forgetting to divide by 2 when calculating depth or distance using reflected pulses: \(2d = vt\).
Concept Misunderstandings
Wave speed changes after reflection because the wave bounces back.
Wave speed depends only on the properties of the medium. Since reflection occurs within the same medium, speed does not change.
Frequency changes after reflection.
Frequency is determined strictly by the vibration frequency of the wave source, which remains unaffected by reflection.
Summary
- A wavefront is a line connecting points in phase; the direction of wave propagation is always perpendicular to it.
- The distance between consecutive wavefronts equals the wavelength, \(\lambda\).
- Law of Reflection: angle of incidence equals angle of reflection, \(i = r\).
- During reflection, frequency, wavelength and wave speed remain unchanged; only the direction of propagation changes.
- For echo or depth calculation, use \(2d = vt\) because the wave travels forward to the reflector and back again.
Short Activity
Objective: Test your understanding of wave reflection, wavefronts and echo calculations.
A. Objective Quiz
1 Which of the following wave characteristics changes when a water wave is reflected by a plane barrier?
2 A pulse of ultrasound travels at \(1\,500\text{ m s}^{-1}\) in water. It is reflected by the seabed and detected after \(120\text{ ms}\). What is the depth of the sea?
B. Fill in the Blanks
3 The direction of wave propagation is always to the wavefront.
4 In reflection of waves, the angle of incidence is always equal to the angle of .
C. Matching / Drag and Drop
Match each step of drawing water wave reflection to its correct description. If using a phone, tap the answer first, then tap the matching box.
