🌊 General Properties of Waves: Core Physics (9223) Study Notes

Hey there! Welcome to the exciting world of waves! This chapter is fundamental because waves—like sound, light, and radio signals—are how energy moves around our universe. Don't worry if some terms look intimidating; we’ll break down every concept into clear, bite-sized chunks. Let’s dive in!

1. What is a Wave?

In physics, a wave is defined simply as a disturbance that transfers energy from one place to another.

  • Key Fact: Waves transfer energy, but they do not permanently transfer the matter (or the medium) through which they travel.
  • The material the wave travels through (like water or air) is called the medium.
Analogy: The Stadium Wave (The "Mexican Wave")

Imagine a stadium doing a 'Mexican wave'. People stand up and sit down (this is the vibration of the matter), but the actual wave travels around the stadium. The people (the matter) stay in their seats, but the energy of the cheer moves forward. This is exactly how physical waves work!

Quick Review: Waves move Energy, not Matter.

2. Types of Waves: Transverse vs. Longitudinal

We classify waves based on how the particles in the medium vibrate compared to the direction the energy is travelling. There are two main types you need to know:

A. Transverse Waves

In a transverse wave, the direction of the vibration is perpendicular (at a 90° angle) to the direction the wave is travelling.

  • Vibration Direction: Up and down.
  • Wave Travel Direction: Side to side.
  • Key Parts: The highest point is the crest (or peak), and the lowest point is the trough.
  • Examples: Water waves (on the surface), all electromagnetic waves (light, radio, X-rays).

Simple Analogy: Imagine shaking a rope up and down. The pulse moves horizontally, but the rope itself moves vertically.

B. Longitudinal Waves

In a longitudinal wave, the direction of the vibration is parallel (in the same direction) to the direction the wave is travelling.

  • Vibration Direction: Back and forth.
  • Wave Travel Direction: Back and forth.
  • Key Parts: Areas where particles are bunched together are compressions. Areas where particles are spread out are rarefactions.
  • Examples: Sound waves, P-waves (a type of earthquake wave).

Memory Trick: Longitudinal waves are waves that travel Lengthwise (parallel).

💡 Did You Know?
Sound waves are vital examples of longitudinal waves. This is why sound needs a medium (like air or water) to travel; the particles must be able to bump into each other to pass the compression along!

3. The Anatomy of a Wave: Essential Definitions

To measure and describe any wave, we use four key terms. Make sure you know these definitions perfectly!

A. Amplitude (\(A\))

The amplitude is the maximum displacement (distance) of a point on the wave from its resting position (the equilibrium line).

  • What it means: Amplitude tells you the energy of the wave.
  • Example: For sound, large amplitude means loud volume. For light, large amplitude means bright light.
B. Wavelength (\(\lambda\))

The wavelength (symbolized by the Greek letter lambda, \(\lambda\)) is the distance between two consecutive, identical points on a wave.

  • For transverse waves: Distance between two crests or two troughs.
  • For longitudinal waves: Distance between two consecutive compressions or two consecutive rarefactions.
  • Units: Wavelength is a distance, so it’s measured in metres (m).
C. Frequency (\(f\))

The frequency is the number of complete waves that pass a fixed point every second.

  • Units: Frequency is measured in Hertz (Hz). (1 Hz = 1 wave per second).
  • Think of "frequent" – how often the waves come.
D. Period (\(T\))

The period is the time taken for one complete wave to pass a fixed point.

  • Units: Measured in seconds (s).
  • The period and frequency are inversely related: $$T = \frac{1}{f}$$

Key Takeaway: Amplitude relates to energy. Wavelength and frequency relate to the wave's shape and speed.

4. Wave Speed and the Fundamental Wave Equation

The wave speed (\(v\)) is the distance a wave travels per unit of time (how quickly the energy moves). Since all waves follow the same basic rules, we can link speed, frequency, and wavelength together using one extremely important equation.

The Wave Equation

The speed of a wave is calculated by multiplying its frequency by its wavelength:

$$v = f\lambda$$

Where:

  • \(v\) = Wave speed (measured in m/s)
  • \(f\) = Frequency (measured in Hz)
  • \(\lambda\) = Wavelength (measured in m)
Step-by-Step Guide to Using the Equation

Don't worry if rearranging equations seems tricky—we can use a simple technique:

1. Identify your knowns: Read the question and write down the two values you are given (\(v\), \(f\), or \(\lambda\)).

2. Check units: Ensure wavelength is in metres (m) and frequency is in Hertz (Hz). If you are given cm, convert to m by dividing by 100.

3. Rearrange if necessary:

  • To find speed: \(v = f \times \lambda\)
  • To find frequency: \(f = \frac{v}{\lambda}\)
  • To find wavelength: \(\lambda = \frac{v}{f}\)
⚠️ Common Mistake Alert
Always remember your units! If a question gives you a time in minutes, you must convert it to seconds. If a length is in cm, convert it to metres before using the wave equation.

5. Core Wave Behaviours

All waves exhibit three basic behaviours when they encounter a boundary or change of medium.

A. Reflection

Reflection occurs when a wave hits a boundary and bounces back.

  • Example: An echo (sound waves reflecting off a wall) or seeing your image in a mirror (light waves reflecting off a surface).
  • Important Rule: The angle the wave hits the surface (angle of incidence) is equal to the angle the wave leaves the surface (angle of reflection).
B. Refraction

Refraction is the change in speed and direction of a wave as it passes from one medium to another (e.g., from air into water).

  • What happens? When a wave slows down (e.g., light entering glass), it usually bends towards the normal line. When it speeds up (e.g., light leaving glass), it bends away.
  • Example: A pencil placed in a glass of water looks broken or bent at the water line because the light path is changing speed and direction.
C. Diffraction

Diffraction is the spreading out of waves as they pass through a narrow opening (an aperture) or around the edge of an obstacle.

  • The amount of spreading is greatest when the size of the gap is similar to the wavelength of the wave.
  • Example: When you hear music from a room, even though you can't see the speaker, that's diffraction! The sound waves are bending around the doorway.

🧠 Quick Review Box: General Properties

  • Transverse: Vibration is Perpendicular (like light).
  • Longitudinal: Vibration is Parallel (like sound).
  • Equation: \(v = f\lambda\)
  • Reflection: Bouncing back (Echoes).
  • Refraction: Bending due to change in speed (Pencil in water).
  • Diffraction: Spreading around corners/gaps (Hearing sound around a door).

You’ve covered the fundamentals of waves! Remember these definitions and the wave equation, and you're well on your way to mastering this topic! Keep practicing!