DP IB Physics: SL
C. Wave Behaviour
C.2 Wave Model
DP IB Physics: SLC. Wave BehaviourC.2 Wave ModelUnderstandings |
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|---|---|
| a) | Transverse and longitudinal travelling waves |
| b) |
Wavelength λ, frequency ƒ, time period T, and wave speed v applied to wave motion as given by [math]v = f \lambda = \frac{\lambda}{T}[/math] |
| c) | The nature of sound waves |
| d) | The nature of electromagnetic waves |
| e) | The differences between mechanical waves and electromagnetic waves |
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a) Types of Travelling Waves
- ⇒ Transverse Waves
- In transverse waves, the particles of the medium vibrate perpendicular to the direction in which the wave travels.
- Example:
- – Waves on a string
- – Light waves (electromagnetic waves)
- – Water surface waves
- Characteristics:
- – If the wave moves left to right, the particles move up and down.
- – They have crests (highest point) and troughs (lowest point).
- ⇒ Longitudinal Waves
- In longitudinal waves, the particles of the medium vibrate parallel to the direction of wave propagation.
- Example:
- – Sound waves in air
- – Compression waves in a spring
- Characteristics:
- – Areas of compression (particles close together) and rarefaction (particles spread out)
- – The motion is like pushing and pulling a slinky back and forth.
- Figure 1 Longitudinal and Transverse waves
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b) Wave Parameters
- Waves are described using these four basic properties:
- ⇒ Wavelength (λ)
- Definition: The distance between two identical points in a wave cycle (e.g., crest to crest or compression to compression)
- Unit: Meters (m)
- ⇒ Frequency (ƒ)
- Definition: The number of wave cycles passing a point per second
- – Unit: Hertz (Hz)
- Formula:
- [math]f = \frac{1}{T}[/math]
- ⇒ Time Period (T)
- Definition: The time it takes for one complete wave cycle to pass a point
- – Unit: Seconds (s)
- Formula:
- [math]T = \frac{1}{f}[/math]
- ⇒ Wave Speed (v)
- Definition: The speed at which the wave moves through the medium
- – Unit: Meters per second (m/s)
- Figure 2 A transvers wave in which has 3-meter wavelength
- ⇒ The Wave Equation
- The wave equation connects speed, wavelength, and frequency:
- [math]v = fλ[/math]
- Or using time period:
- [math]v = \frac{λ}{f}[/math]
- ⇒ Explanation:
- – λ (wavelength): How far one wave travels
- – f (frequency): How many waves happen per second
- – T (time period): How long one wave takes
- So:
- A longer wavelength or higher frequency means the wave travels faster.
- If you increase frequency while keeping speed constant, wavelength gets shorter (and vice versa).
- Example – Sound in Air
- Imagine a sound wave with:
- – Frequency: f=440 Hz (a musical “A” note)
- – Speed of sound: v=340 m/s
- Using the wave equation:
- [math]\lambda = \frac{v}{f} \\
\lambda = \frac{340}{4} \\
\lambda \approx 0.773 \ \text{m}[/math] - So, each sound wave is about 77.3 cm long.
- Figure 3 Sound waves on air
- ⇒ Differences Between Transverse & Longitudinal Waves
| Feature | Transverse Waves | Longitudinal Waves |
|---|---|---|
| Particle motion | Perpendicular to wave | Parallel to wave |
| Seen in | Light, string, water | Sound, spring, seismic P-waves |
| Parts of the wave | Crest & Trough | Compression & Rarefaction |
| Medium requirement | Can travel in vacuum (EM waves) | Needs a medium (e.g., air, solid) |
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C) The Nature of Sound Waves - Sound waves are mechanical waves produced by vibrating objects. They travel through a medium (like air, water, or solids) by causing particles in the medium to vibrate.
- ⇒ Type of Wave: Longitudinal
- Sound waves are primarily longitudinal waves:
- – The particles of the medium vibrate parallel to the direction of the wave’s motion.
- – They consist of compressions (high pressure) and rarefactions (low pressure).
- ⇒ Example:
- Imagine a slinky. Push one end forward and release — you’ll see areas where the coils bunch up (compression) and spread out (rarefaction). That’s how sound behaves in air.
- ⇒ Sound is Produced
- Sound begins with vibration:
- A vibrating object (like vocal cords, a speaker cone, or guitar string) disturbs nearby air particles.
- These vibrations cause air molecules to oscillate, transmitting energy from one to another — creating a wave.
- The disturbance travels outward in all directions — this is the sound wave.
- ⇒ Propagation of Sound:
- Sound moves by transferring energy from one particle to the next:
- In air, molecules bump into their neighbors, creating zones of compression and rarefaction.
- In solids, sound travels via particle vibrations in the lattice structure.
- In liquids, molecules are closer than in gases, so sound often travels faster than in air.
- ⇒ Speed of Sound in Different Media
| Medium | Approx. Speed (m/s) |
|---|---|
| Air (20°C) | 343 |
| Water | 1,480 |
| Steel | 5,960 |
| Vacuum | 0 (no sound) |
- Sound travels fastest in solids, slower in liquids, and slowest in gases, because particle density and bonding affect how fast vibrations pass through.
- Figure 4 Speed of wave in different mediums
- ⇒ Properties of Sound Waves
| Property | Description |
|---|---|
| Frequency (f) | Number of vibrations per second (in Hz). Determines pitch. |
| Wavelength (λ) | Distance between two compressions or rarefactions. |
| Amplitude | How much particles are displaced. Determines loudness. |
| Speed (v) | How fast the wave moves through the medium. |
| Time Period (T) | Time taken for one complete cycle.
[math]T = \frac{1}{f}[/math] |
| Wave Equation | [math]v = fλ[/math] (same as any mechanical wave) |
- ⇒ Audible and Inaudible Sound
- Audible range (for humans):
- Hz – 20,000 Hz
- Below 20 Hz: Infrasound (e.g., earthquakes, elephants)
- Above 20,000 Hz: Ultrasound (e.g., bats, medical imaging)
- ⇒ Reflection, Refraction, and Diffraction of Sound
- Just like light, sound waves also:
- Reflect (echo off walls)
- Refract (change direction when entering a new medium)
- Diffract (bend around corners or through gaps)
- Figure 5 Reflection, Refraction and diffraction of sound
- This is why you can hear someone talking around a corner even if you can’t see them.
- ⇒ Echo and Reverberation
- Echo: A distinct reflected sound heard after a delay (≥ 0.1 seconds).
- Reverberation: Multiple reflections that blend together and create a prolonged sound.
- Used in designing concert halls and recording studios for sound clarity.
- ⇒ Applications of Sound Waves
- – Communication: Speech, music, sonar, telephones
- – Medicine: Ultrasound for imaging (e.g., fetal scans)
- – Navigation: Bats and dolphins use echolocation
- – Industry: Detecting cracks via ultrasonic testing
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d) The Nature of Electromagnetic Waves
- Electromagnetic waves are waves of energy that consist of oscillating electric and magnetic fields, which are perpendicular to each other and also to the direction in which the wave is traveling.
- – They are transverse waves.
- – They can travel through vacuum (unlike sound waves), which is why we can see light from the Sun even though space is empty.
- ⇒ EM Waves Produced:
- Electromagnetic waves are produced when:
- – A charged particle accelerates, or
- – An electric current changes direction, like in an antenna.
- This motion generates:
- An electric field (E).
- A magnetic field (B), both of which keep regenerating each other as the wave propagates.
- Figure 6 Electromagnetic wave
- ⇒ Characteristics of EM Waves
| Property | Description |
|---|---|
| Transverse | Electric and magnetic fields vibrate perpendicular to wave travel. |
| Can travel in vacuum | They do not need a medium (can travel in space). |
| Self-propagating | The changing electric field creates a magnetic field and vice versa. |
| Speed in vacuum | [math]c = 3 × 10^8 m/s[/math] |
| Wave equation | [math]c = fλ[/math] where ccc is the speed of light. |
- – E-field oscillates up and down,
- – B-field oscillates side to side,
- – Wave moves forward, forming a 3D structure.
- ⇒ The Electromagnetic Spectrum
- Electromagnetic waves come in a spectrum of frequencies and wavelengths:
| Type | Wavelength | Frequency | Common Uses |
|---|---|---|---|
| Radio Waves | > 1 m | < [math]10^9[/math] Hz | Broadcasting, communication |
| Microwaves | 1 mm – 1 m | [math]10^9 – 10^{12}[/math]Hz | Cooking, radar, mobile phones |
| Infrared (IR) | 700 nm – 1 mm | [math]10^{12} – 10^{14}[/math]Hz | Remote controls, thermal cameras |
| Visible Light | 400–700 nm | [math]10^{14}[/math]Hz | Human vision, photography |
| Ultraviolet (UV) | 10–400 nm | [math]10^{15}[/math]Hz | Sterilization, sunburn |
| X-rays | < 10 nm | [math]10^{16}[/math]Hz | Medical imaging |
| Gamma Rays | < 0.01 nm | > [math]10^{18}[/math] Hz | Cancer treatment, nuclear reactions |
- ⇒ Properties of EM Waves
- – Reflection – bounce off surfaces (like a mirror)
- – Refraction – bend when entering a different medium (like a lens)
- – Diffraction – bend around corners
- – Interference – when waves overlap and combine
- – Polarization – orientation of the electric field
- ⇒ Nature of Electromagnetic Waves
- Transverse waves
- – Travel through vacuum or matter
- – Made of oscillating electric and magnetic fields
- – Travel at the speed of light in vacuum
- – Vary across a wide spectrum with different uses
- Figure 7 Electromagnetic spectrum
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e) Differences Between Mechanical Waves and Electromagnetic Waves
| Feature | Mechanical Waves | Electromagnetic Waves |
|---|---|---|
| Medium required? | Yes – need a medium (air, water, solid) | No – can travel through vacuum |
| Type | Can be transverse or longitudinal | Always transverse |
| Speed | Depends on the medium (slower in gases) | Speed in vacuum = [math]3.00 × 10^8 m/s[/math] |
| How generated | Vibration of particles | Accelerating charges |
| Examples | Sound, water waves, seismic waves | Light, radio waves, X-rays |
| Energy transfer | Through particle interaction | Through electric & magnetic field oscillations |
| Affected by vacuum | Cannot propagate in vacuum | Easily propagate through vacuum |
| Frequency range | Limited (e.g. sound: 20 Hz–20 kHz) | Extremely wide (radio to gamma rays) |