Mastering Properties of Waves
CSEC Physics: Waves & Energy
Essential Understanding: Waves are a method of transferring energy from one place to another without transferring matter. Whether it’s the sound of music, the light from the sun, or the ripples in a pond, understanding Amplitude, Wavelength, and Frequency is key to mastering the physical world.
Core Concepts
Transverse Waves
Definition: Waves where the particle vibration is perpendicular (at 90°) to the direction of energy transfer.
Examples: Light waves, Water ripples, Waves on a string.
Key Terms: Crest (peak), Trough (valley).
Longitudinal Waves
Definition: Waves where the particle vibration is parallel to the direction of energy transfer.
Examples: Sound waves, Primary (P) seismic waves.
Key Terms: Compression (high pressure), Rarefaction (low pressure).
Amplitude
Definition: The maximum displacement of a particle from its rest position.
Physical Meaning: Relates to the energy and loudness (sound) or brightness (light) of the wave.
Symbol: \( A \) (Unit: meters, m)
Wavelength (\( \lambda \))
Definition: The distance between two consecutive similar points in phase (e.g., crest to crest, compression to compression).
Unit: meters (m).
Frequency (\( f \))
Definition: The number of complete waves passing a point per second.
Unit: Hertz (Hz). \( 1 \text{ Hz} = 1 \text{ vibration/s} \).
Related: Period (\( T \)) is the time for one wave: \( T = \frac{1}{f} \).
The Wave Equation
This is the most important formula in this topic. It connects the speed of the wave to its frequency and wavelength.
- \( v \): Wave speed (m/s)
- \( f \): Frequency (Hz)
- \( \lambda \): Wavelength (m)
Interactive Wave Lab
Transverse Wave Simulator
Objective: Observe how changing Amplitude and Frequency affects the shape of a transverse wave. Notice that the green dots (particles) only move up and down, while the wave moves right.
Current Amplitude
50 px
Current Frequency
2.0 Hz
Displacement-Distance vs. Displacement-Time
CSEC exams often test your ability to distinguish between a “snapshot” of a wave and the movement of a single particle. The chart below compares these two critical perspectives.
Analysis: Blue Line (Displacement-Distance): Shows the shape of the wave at one instant in time. The distance between peaks is the Wavelength.
Orange Line (Displacement-Time): Shows the movement of one single point over time. The distance between peaks is the Period (\( T \)).
Worked Example: Calculating Speed
A water wave has a frequency of 4 Hz and a wavelength of 0.5 m. Calculate the speed of the wave.
Key Examination Insights
Common Mistakes
- Confusing the Period (\( T \)) with Frequency. Remember \( f = \frac{1}{T} \).
- Forgetting unit conversions: kHz to Hz (x 1000) or cm to m ( / 100).
- Assuming particles move along with the wave. In all mechanical waves, matter only oscillates; energy moves forward.
Success Strategies
- For longitudinal diagrams, label Compressions (C) where particles are close and Rarefactions (R) where they are far apart.
- When given a diagram, count the number of cycles carefully to find wavelength.
- Always check if the wave is “Frozen” (Distance graph) or “Moving” (Time graph).
CSEC Practice Arena
Test Your Understanding
\( \lambda = \frac{300}{150} = 2 \, \text{m} \).
CSEC Examination Mastery Tip
Graph Interpretation: In multiple-choice questions, you will often be shown a graph.
- Look at the X-axis label first.
- If it says Distance (m): You are looking at the wave shape. The peak-to-peak distance is Wavelength (\( \lambda \)).
- If it says Time (s): You are looking at one particle oscillating. The peak-to-peak distance is Period (\( T \)).
- Once you identify the x-axis, you can instantly calculate Frequency (\( f = 1/T \)) or confirm Wavelength.