General Properties of Waves: Comprehensive Study Notes (Physics 9203)
Hello future Physicists! Waves are everywhere—from the ripples in a pond to the invisible signals that power your phone. Understanding the general properties of waves is essential because these rules apply to all waves, whether it's light, sound, or water! This chapter lays the crucial foundation for everything we will study later in the "Waves" section. Let's dive in!
Section 1: What is a Wave?
The Key Function of Waves
A wave is a disturbance that transfers energy from one place to another. But here is the most important idea:
- Waves transfer energy.
- Waves do not transfer matter (mass) permanently.
Imagine a crowd doing "the wave" in a stadium. The disturbance (the energy) moves all the way around the stadium, but the people (the matter) only move slightly up and down, returning to their original seats. That’s exactly how physical waves work!
Quick Review: Energy Transfer
Important Point: When a wave travels through a material (a medium), the particles in that medium only vibrate temporarily; they do not travel along with the wave.
Section 2: The Two Main Types of Waves
Waves are classified based on how the particles in the medium vibrate compared to the direction the energy is travelling.
1. Transverse Waves
In a transverse wave, the direction of vibration is at right angles (perpendicular) to the direction the energy is travelling.
- Analogy: Picture shaking a rope up and down. The wave moves horizontally along the floor, but your hand and the rope particles move vertically (up and down).
- Examples: All electromagnetic waves (light, radio waves, X-rays), ripples on water, waves on a string.
- Key Features: They have peaks called crests and valleys called troughs.
Memory Aid: A Transverse wave is like a cross (T) – movement is perpendicular!
2. Longitudinal Waves
In a longitudinal wave, the direction of vibration is parallel to the direction the energy is travelling.
- Analogy: Imagine pushing and pulling a Slinky back and forth. The wave moves horizontally, and the coils (particles) also move horizontally, back and forth in the same direction.
- Example: Sound waves. Sound travels by making air molecules vibrate back and forth.
- Key Features: They have areas where the particles are bunched together (compressions) and areas where they are spread out (rarefactions).
Accessibility Tip: The key difference is the angle. Right angle = Transverse. Same direction = Longitudinal.
Section 3: Key Wave Terminology (The Anatomy of a Wave)
We use specific terms and symbols to describe the size, speed, and timing of waves.
1. Wavelength (\(\lambda\))
Definition: The distance between two identical points on consecutive waves. For example, the distance from one crest to the next crest, or one compression to the next compression.
Symbol: \(\lambda\) (the Greek letter lambda)
Units: Metres (m)
2. Amplitude (A)
Definition: The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium (rest) position.
What it relates to: The amplitude is related to the energy the wave carries. A bigger amplitude means more energy (e.g., a louder sound or a taller water wave).
Units: Metres (m)
3. Frequency (\(f\))
Definition: The number of complete waves that pass a fixed point per second.
Symbol: \(f\)
Units: Hertz (Hz). \(1 \text{ Hz} = 1 \text{ wave per second}\).
4. Period (\(T\))
Definition: The time it takes for one complete wave to pass a fixed point.
Symbol: \(T\)
Units: Seconds (s)
Relationship: Period and Frequency are inverses of each other:
$$T = \frac{1}{f} \quad \text{and} \quad f = \frac{1}{T}$$Section 4: The Wave Speed Equation
The speed of a wave (\(v\)) depends on how far apart the waves are (\(\lambda\)) and how frequently they pass (\(f\)).
The Fundamental Wave Equation
Wave speed is calculated by multiplying the frequency by the wavelength:
$$v = f \times \lambda$$Where:
- \(v\) = Wave speed (m/s)
- \(f\) = Frequency (Hz)
- \(\lambda\) = Wavelength (m)
Step-by-Step Calculation Guide
- Write the Formula: Start every time by writing \(v = f\lambda\).
- Check Units: Ensure the wavelength is in metres (m) and the frequency is in Hertz (Hz). If they are in cm or kHz, convert them first!
- Substitute and Calculate: Plug the numbers into the equation.
Example: A sound wave has a frequency of 500 Hz and a wavelength of 0.66 m. What is its speed?
$$v = 500 \text{ Hz} \times 0.66 \text{ m}$$
$$v = 330 \text{ m/s}$$
Rearranging the Equation
Sometimes you need to find \(f\) or \(\lambda\). It helps to use a formula triangle (or just algebra!):
$$f = \frac{v}{\lambda}$$ $$\lambda = \frac{v}{f}$$
Common Mistake to Avoid: Not converting units! If a wavelength is given in centimetres (cm), you must divide by 100 to get metres (m) before using the wave speed equation.
Section 5: Wave Interactions (Reflection, Refraction, and Diffraction)
When waves meet a boundary, change mediums, or encounter an obstacle, they interact in predictable ways.
1. Reflection
Definition: Reflection occurs when a wave bounces back from a surface or boundary.
Examples: Light bouncing off a mirror, sound waves creating an echo, or water waves hitting a sea wall.
The Law of Reflection:
The angle of incidence (\(i\)) is equal to the angle of reflection (\(r\)).
$$i = r$$
(Both angles are measured relative to the normal—an imaginary line drawn perpendicular to the surface at the point of incidence.)
2. Refraction
Definition: Refraction is the change in direction (bending) of a wave when it passes from one medium to another (e.g., from air to water, or glass to air).
Why does it happen? The change in direction is caused by the wave changing its speed as it enters the new medium.
- If the wave slows down (e.g., light entering glass), it bends towards the normal.
- If the wave speeds up (e.g., light leaving glass), it bends away from the normal.
Real-World Example: A pencil placed in a glass of water looks broken or bent at the water line because the light waves are refracting.
3. Diffraction
Definition: Diffraction is the spreading out of waves as they pass through a gap (aperture) or move around the edge of an obstacle.
Key Rule for Diffraction:
Diffraction is most noticeable (most effective) when the size of the gap is similar to the wavelength of the wave.
Did you know? This is why you can hear someone talking around a corner, even if you can't see them! Sound waves have relatively large wavelengths and diffract easily around everyday objects. Light waves have tiny wavelengths and therefore don't diffract much around small corners, which is why we cannot see around corners.
Chapter Summary: Key Takeaways
- Waves transfer energy, not matter.
- Transverse waves (like light) vibrate perpendicular to the energy direction.
- Longitudinal waves (like sound) vibrate parallel to the energy direction.
- The fundamental relationship governing all waves is the Wave Equation: \(v = f\lambda\).
- Waves interact via Reflection (bouncing back), Refraction (bending due to speed change), and Diffraction (spreading out).
Keep practising those definitions and the wave equation! You’ve got this!