1. Definitions
Wave Motion
A wave is a disturbance which travels through a medium, transferring energy from one point to another without causing any permanent displacement of the medium itself.
Mechanical Waves vs. Electromagnetic Waves
Mechanical waves require a physical material medium for propagation (e.g., sound waves, water waves). Electromagnetic waves do not require any material medium and can travel through a vacuum (e.g., light waves, radio waves, X-rays).
Transverse vs. Longitudinal Waves
In a transverse wave, the particles of the medium vibrate perpendicular to the direction of wave travel (forming crests and troughs). In a longitudinal wave, particles vibrate parallel to the direction of wave travel (forming compressions and rarefactions).
2. Fundamental Wave Phenomena
All classic wave types display five core structural behaviors when interacting with environments:
- Reflection: The bouncing back of a wave train when it hits a barrier surface.
- Refraction: The bending of a wave's direction as it crosses into a medium of different density, changing its speed and wavelength while frequency stays constant.
- Diffraction: The spreading out of wave fronts around edges, corners, or narrow openings.
- Interference: The superposition of two matching wave trains meeting in a medium to form a reinforced or cancelled resultant wave.
- Polarization: The restriction of a transverse wave's vibrations to a single plane (longitudinal waves cannot be polarized).
4. Explanation of Symbols & Wave Parameters
- v = Wave velocity or speed of propagation (measured in meters per second, m/s).
- f = Wave frequency; the number of complete cycles per second (measured in Hertz, Hz or s¹).
- λ (Lambda) = Wavelength; distance between two successive crests or matching points (measured in meters, m).
- T = Period; time taken for one single complete cycle to pass a fixed point (measured in seconds, s).
- A = Amplitude; maximum displacement of a particle from its rest position (measured in meters, m).
Understanding the Mechanics:
When a wave moves from one medium to a denser or rarer medium (such as light passing from air into a glass block), its frequency never changes because it depends strictly on the source creating the disturbance. However, its velocity and wavelength adapt proportionally according to the wave equation.
5. WAEC Objective Practice Questions (Interactive)
Click on an option to check if your answer is correct. Explanations will automatically reveal themselves.
1. Which of the following wave types can travel through a vacuum?
A. Sound waves
B. Water waves
C. Radio waves
D. Waves propagating down a stretched guitar string
Explanation: Radio waves are electromagnetic waves. Unlike mechanical waves, electromagnetic waves do not require a material medium and propagate perfectly through empty space.
2. In a transverse wave, the particles of the medium vibrate in what pattern relative to the direction of propagation?
A. Parallel to the energy propagation path
B. Perpendicular to the direction of wave travel
C. In concentric circular patterns ahead of the wave front
D. Randomly throughout the medium boundary
Explanation: Transverse waves feature particle oscillations that occur exactly at right angles (90 degrees or perpendicular) to the directional motion of the wave front.
3. Which of the following properties distinguishes a transverse wave from a longitudinal wave?
A. Reflection
B. Refraction
C. Diffraction
D. Polarization
Explanation: Only transverse waves can be polarized because their oscillations are perpendicular to the travel path. Longitudinal waves cannot be restricted to a single plane of vibration.
4. Calculate the frequency of a water wave whose wavelength is 4.0 m and travels at a speed of 12.0 m/s.
A. 48.0 Hz
B. 3.0 Hz
C. 0.33 Hz
D. 16.0 Hz
Explanation: Using the wave equation v = f × λ, isolating frequency yields f = v / λ. Substituting values: f = 12.0 / 4.0 = 3.0 Hz.
5. When a wave profile passes from deep water into shallow water, its velocity decreases. What happens to its frequency?
A. It increases proportionally
B. It decreases proportionally
C. It remains constant
D. It drops immediately to zero
Explanation: Frequency is determined solely by the original vibratory source creating the wave. When crossing medium boundaries, velocity and wavelength change, but frequency stays identical.
6. The distance between two successive wave crests is 20 cm. If the period of the wave is 0.5 seconds, calculate the wave speed.
A. 0.40 m/s
B. 10.0 m/s
C. 40.0 m/s
D. 4.00 m/s
Explanation: Convert wavelength to SI units: 20 cm = 0.2 m. Calculate frequency: f = 1 / T = 1 / 0.5 = 2 Hz. Find velocity: v = f × λ = 2 × 0.2 = 0.4 m/s.
7. The spreading out of a wave front as it passes through a narrow gap or around an obstacle boundary is termed:
A. Interference
B. Reflection
C. Diffraction
D. Refraction
Explanation: Diffraction describes the fundamental bent flaring behavior of wave energy when squeezing through narrow slots or skirting physical geometric edges.
8. What wave state is produced by the superposition of two matching wave trains of equal amplitude and frequency travelling in opposite directions?
A. Progressive wave
B. Stationary (Standing) wave
C. Polarized plane wave
D. Refracted compression wave
Explanation: When two identical waves meet travelling in exactly opposite directions, they combine to produce stable nodes and antinodes, forming a stationary (standing) wave profile.
9. The maximum displacement of a vibrating particle in a medium from its mean equilibrium position is its:
A. Amplitude
B. Wavelength
C. Wave crest height
D. Phase constant
Explanation: Amplitude is defined as the maximum peak range limit a particle swings out from its calm center point of rest.
10. A wave generator produces 60 complete structural cycles in a time window of 5.0 seconds. Determine the period of the wave.
A. 12.00 s
B. 0.08 s
C. 0.12 s
D. 300.00 s
Explanation: Period (T) is total time divided by total number of completed cycles. T = 5.0 seconds / 60 cycles = 0.0833 seconds.
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