Combined Science (9204) | Waves

Welcome to the World of Waves!

Hello future scientist! This chapter is all about Waves – one of the most fundamental concepts in Physics. Waves are everywhere, from the sound you hear and the light you see, to the signals that power your phone.

Don't worry if this topic feels a little abstract at first. We will break down complicated ideas like wavelength and frequency using simple analogies, making sure you understand exactly how energy travels across the universe. Let's dive in!

What Exactly is a Wave?

In physics, a wave is defined as a disturbance that transfers energy from one place to another without transferring matter.

• Imagine watching a crowd at a sports stadium doing a "Mexican Wave." The wave moves around the stadium, but the people (the matter) stay in their seats.
• When a wave travels across water, the water molecules mostly move up and down, but the energy moves forward.

Key Takeaway: Waves transfer Energy, not matter.

Section 1: The Two Main Types of Waves

We classify waves based on the direction the particles of the medium (the stuff the wave travels through) move compared to the direction the energy moves.

1. Transverse Waves

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

• Movement: The particles move up and down while the energy moves forwards.
• Shape: They have peaks (crests) and valleys (troughs).
• Examples: All Electromagnetic (EM) waves (like light and radio), and ripples on water.

Analogy for Transverse Waves

Imagine shaking a rope up and down. The pulse moves along the rope (forward), but the rope itself just moves up and down (perpendicular).

2. Longitudinal Waves

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

• Movement: The particles move back and forth.
• Shape: They create areas where the particles are bunched up (compressions) and areas where they are spread out (rarefactions).
• Example: Sound waves.

Analogy for Longitudinal Waves

Imagine pushing and pulling a Slinky toy quickly. The squished part (compression) moves along the Slinky in the same direction you pushed it.

Section 2: Key Vocabulary and Measurements

To measure and describe waves, we need specific vocabulary. These terms apply to both transverse and longitudinal waves.

1. Amplitude (A)

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

• What it tells you: Amplitude is related to the amount of energy the wave carries. A bigger amplitude means more energy (e.g., a loud sound or a bright light).
• Measurement: Usually measured in metres (m).

2. 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 from one peak to the next peak, or one trough to the next trough.
• For longitudinal waves: Distance from one compression to the next compression.
• Measurement: Measured in metres (m).

3. Frequency (f)

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

• Measurement: Measured in Hertz (Hz). \(1 \text{ Hz} = 1\) wave per second.

4. Period (T)

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

$$T = \frac{1}{f}$$

• Measurement: Measured in seconds (s).

Section 3: The Wave Equation (Speed)

The speed at which a wave travels depends on its frequency and its wavelength. This relationship is crucial for calculations.

The Key Formula

The wave speed (\(v\)) is calculated by multiplying the frequency (\(f\)) by the wavelength (\(\lambda\)).

$$\mathbf{v = f \lambda}$$

Where:
\(v\) = Wave speed (metres per second, m/s)
\(f\) = Frequency (Hertz, Hz)
\(\lambda\) = Wavelength (metres, m)

Memory Aid: "Velocity equals Frequency times Lambda"

Think of it as Victoria Felt Lazy!

Step-by-Step Example Calculation

Question: A sound wave has a frequency of 500 Hz and a wavelength of 0.66 metres. What is the speed of the wave?

1. Identify the known values:
   \(f = 500 \text{ Hz}\)
   \(\lambda = 0.66 \text{ m}\)
2. Write down the formula:
   \(v = f \lambda\)
3. Substitute the values and calculate:
   \(v = 500 \times 0.66\)
   \(v = 330\)
4. State the final answer with units:
   The wave speed is \(330 \text{ m/s}\).

Common Mistake to Avoid: Always ensure your wavelength is in metres (m) and your frequency is in Hertz (Hz) before calculating speed!

Section 4: The Electromagnetic Spectrum

The Electromagnetic Spectrum (EM) is the full range of electromagnetic waves. Crucially, all EM waves are transverse waves and travel at the same speed in a vacuum (the speed of light, \(c\)).

Key Properties of EM Waves

• They all travel at \(3.0 \times 10^8 \text{ m/s}\) in a vacuum.
• They can travel through a vacuum (empty space), unlike sound waves.
• The only difference between them is their wavelength and frequency.

Order of the Spectrum

The EM spectrum is ordered by increasing frequency and decreasing wavelength. (High frequency means short wavelength, and vice versa.)

Long Wavelength / Low Frequency \(\rightarrow\) Short Wavelength / High Frequency

Memory Aid for Order (Low Frequency to High Frequency)

Radio Microwaves Infrared Visible Ultraviolet X-rays Gamma
Radiant Men In Vacations Use Xtra Glasses

Let's look at the seven types, their main uses, and their potential dangers:

1. Radio Waves

• Uses: Communication (TV, radio broadcasting), satellite transmission.
• Dangers: Generally considered low risk due to low energy.

2. Microwaves

• Uses: Heating food (microwave ovens), satellite communications, mobile phones.
• Dangers: Can cause internal heating in human tissue if intensity is too high.

3. Infrared (IR)

• Uses: Electrical heaters, cooking (grills), thermal imaging cameras (night vision), remote controls.
• Dangers: Intense infrared can cause skin burns.

4. Visible Light

• Uses: Seeing, photography, optical fibres (for internet/data).
• Dangers: Very bright light sources can cause eye damage.

5. Ultraviolet (UV)

• Uses: Tanning beds, security marking (fluorescence), sterilizing equipment.
• Dangers: Can cause skin cancer (melanoma) and eye damage (cataracts). This is why sunscreen is important!

6. X-rays

• Uses: Medical imaging (seeing broken bones), checking airport luggage.
• Dangers: Highly penetrating, can cause cell mutation and cancer. Used sparingly and with protection (lead).

7. Gamma Rays

• Uses: Sterilizing medical equipment, killing cancer cells (radiotherapy), tracing industrial leaks.
• Dangers: Most penetrating and damaging form of radiation; highly dangerous to living cells.

Key Takeaway (EM Spectrum): All EM waves travel at the speed of light in a vacuum. Moving from Radio to Gamma, the wavelength decreases, and the frequency (and energy) increases.

Section 5: Sound Waves (A Quick Look)

Sound is a mechanical wave, meaning it requires a medium (like air, water, or solids) to travel. It cannot travel through a vacuum (which is why space is silent!).

• Type: Sound waves are longitudinal waves.
• Mechanism: Sound travels by creating vibrations that push the particles in the medium together (compressions) and pull them apart (rarefactions).
• Speed: Sound travels fastest through solids, slower through liquids, and slowest through gases (like air). For example, sound travels at about 330 m/s in air, but much faster in steel!

The pitch of a sound is determined by its frequency (higher frequency = higher pitch). The loudness of a sound is determined by its amplitude (larger amplitude = louder sound).

Congratulations!

You have covered the fundamentals of waves, including their types, measurements, the essential wave equation, and the entire electromagnetic spectrum. Keep practicing those definitions and the wave speed formula, and you'll master this chapter in no time!