CIE iGCSE Co-ordinated Sciences-P3.1 General properties of waves - Study Notes- New Syllabus
CIE iGCSE Co-ordinated Sciences-P3.1 General properties of waves – Study Notes
CIE iGCSE Co-ordinated Sciences-P3.1 General properties of waves – Study Notes -CIE iGCSE Co-ordinated Sciences – per latest Syllabus.
Key Concepts:
Core
1. Know that waves transfer energy without transferring matter
2. Describe what is meant by wave motion as illustrated by vibration (oscillation) in ropes and springs and by experiments using water waves
3. Describe the features of a wave in terms of wavelength, frequency, crest (peak), trough, amplitude and wave speed
4. Describe how waves can undergo:
(a) reflection at a plane surface
(b) refraction due to a change of speed
5. Recall and use the equation for wave speed $( v = f \lambda )$
Supplement
6. Know that for a transverse wave, the direction of vibration is at right angles to the direction of propagation and understand that electromagnetic radiation, water waves and seismic S-waves (secondary) are transverse
7. Know that for a longitudinal wave, the direction of vibration is parallel to the direction of propagation and understand that sound waves and seismic P-waves (primary) are longitudinal
8. Describe how waves undergo diffraction through a narrow gap
9. Describe how wavelength and gap size affects diffraction through a gap
CIE iGCSE Co-Ordinated Sciences-Concise Summary Notes- All Topics
Waves and Energy Transfer
Waves are vibrations or oscillations that travel through a medium (such as air, water, or a solid) or even through space (in the case of electromagnetic waves). They transfer energy from one point to another without transferring matter.
Explanation:
- In a wave, particles of the medium only vibrate about their mean positions.
- The particles themselves do not travel with the wave; instead, the disturbance (energy) moves forward.
- For example:
- Sound waves transfer energy through vibrating air molecules, but the air itself does not move forward with the wave.
- Water waves make water particles move in circular or up–down motions, but the water does not travel across the pond or ocean with the wave.
Example:
A floating cork on water bobs up and down as ripples pass across the surface. Does the cork move with the wave to the edge of the pond?
▶️Answer/Explanation
No, the cork stays roughly in the same place, only moving up and down. This shows that the water waves transfer energy across the pond, but not the water itself (no net transfer of matter).
Wave Motion
Wave motion is the transfer of energy from one point to another by vibrations or oscillations, without the transfer of matter.
Key Idea:
The medium’s particles only oscillate (vibrate) about their equilibrium positions; the disturbance (energy) moves forward, not the material itself.
Illustrations of Wave Motion:
Ropes and Springs (mechanical waves):
- If one end of a rope is shaken up and down, a disturbance travels along the rope.
- The rope particles move up and down (oscillations), but the pulse (energy) moves forward.
- Similarly, compressing and releasing a spring produces compressions and rarefactions that travel along it.
Water Waves:
- Dropping a stone into water produces ripples that spread outward.
- Water particles move in small circles or up–down paths but do not travel across the pond.
- The ripples transfer energy across the surface.
Example:
A student ties a rope to a wall and gives one quick jerk upward at the free end. A wave pulse travels along the rope and reflects back when it reaches the wall. Did the rope itself move from one end to the other?
▶️Answer/Explanation
No, the rope itself stays in place. Only the disturbance (the wave pulse) travels along the rope. This demonstrates that waves transfer energy (the jerk) without transferring the material (rope).
Features of a Wave
Waves have several key features that describe their size, shape, and how they transfer energy:
Crest (Peak): The highest point of a wave above the rest (equilibrium) position.
Trough: The lowest point of a wave below the rest position.
Amplitude (A): The maximum displacement of a particle from the rest position. It measures the wave’s energy (larger amplitude → more energy).
Wavelength (λ): The distance between two consecutive crests or two consecutive troughs (or any repeating point on the wave). It is measured in metres (m).
Frequency (f): The number of waves produced per second, or the number of complete cycles passing a point each second. Measured in hertz (Hz).
Wave Speed (v): The distance a wave travels per second. Related to frequency and wavelength by the equation:
Equation: \( v = f \lambda \)
Visual Description:
Imagine a rope wave: the crests are the “hills”, the troughs are the “valleys”, the amplitude is the height of a hill, and the wavelength is the distance between two hills. Frequency is how many hills pass a fixed point in one second.
Example
A water wave has a wavelength of \( 0.5~\text{m} \) and a frequency of \( 4~\text{Hz} \). Calculate:
- The wave speed
- The number of waves passing a point in 3 seconds
▶️Answer/Explanation
Step (1) – Wave speed:
Using \( v = f \lambda \):
\( v = 4 \times 0.5 = 2.0~\text{m/s} \).
Step (2) – Number of waves in 3 s:
Frequency = 4 waves per second → in 3 seconds: \( 4 \times 3 = 12 \) waves.
Final Answer:
Wave speed = \( 2.0~\text{m/s} \); Number of waves = 12.
Wave Behaviours: Reflection and Refraction
(a) Reflection at a Plane Surface
When a wave (light, sound, or water wave) strikes a flat surface (mirror, hard wall, etc.), it is bounced back into the original medium. The direction of the wave changes, but its speed, frequency, and wavelength remain the same.
- Law of Reflection: Angle of incidence = Angle of reflection.
- The incident ray, reflected ray, and the normal (a perpendicular line to the surface) all lie in the same plane.
Example: Light waves reflecting from a mirror, producing an image.
(b) Refraction due to a Change of Speed
Refraction occurs when a wave passes from one medium into another, causing a change in speed. This usually results in a change of direction (bending of the wave).
- If the wave slows down (e.g. air → glass), it bends towards the normal.
- If the wave speeds up (e.g. glass → air), it bends away from the normal.
- Frequency remains constant, but wavelength changes because \( v = f \lambda \).
Example: A straw in water looks “bent” because light refracts when passing from water into air.
Example
A light ray enters glass from air at an angle of incidence of \( 30^\circ \). If its speed in air is \( 3.0 \times 10^8~\text{m/s} \) and in glass is \( 2.0 \times 10^8~\text{m/s} \), calculate:
- The refractive index of glass
- The angle of refraction inside the glass
▶️Answer/Explanation
Step (1) – Refractive index:
\( n = \dfrac{c}{v} = \dfrac{3.0 \times 10^8}{2.0 \times 10^8} = 1.5 \).
Step (2) – Use Snell’s Law:
\( n_1 \sin \theta_1 = n_2 \sin \theta_2 \).
Here, \( n_1 = 1.0 \) (air), \( \theta_1 = 30^\circ \), \( n_2 = 1.5 \).
\( \sin \theta_2 = \dfrac{n_1 \sin \theta_1}{n_2} = \dfrac{1.0 \times \sin 30^\circ}{1.5} = \dfrac{0.5}{1.5} = 0.333 \).
So, \( \theta_2 = \sin^{-1}(0.333) \approx 19.5^\circ \).
Final Answer:
(a) Refractive index = \( 1.5 \).
(b) Angle of refraction ≈ \( 19.5^\circ \).
Wave Speed Equation
For any wave: \( v = f\lambda \),
where
- \( v \) is wave speed (m/s),
- \( f \) is frequency (Hz), and
- \( \lambda \) is wavelength (m).
Example:
At a pier, \( 8 \) wave crests pass a fixed point in \( 20~\text{s} \). The measured distance between the first and the fifth crest is \( 56~\text{m} \). Find the wave speed \( v \).
▶️Answer/Explanation
Step 1 – Frequency: \( f = \dfrac{\text{number of crests}}{\text{time}} = \dfrac{8}{20} = 0.40~\text{Hz} \).
Step 2 – Wavelength: From the first to the fifth crest there are \( 4 \) wavelengths, so \( \lambda = \dfrac{56}{4} = 14~\text{m} \).
Step 3 – Speed: \( v = f\lambda = 0.40 \times 14 = 5.6~\text{m/s} \).
Final: \( v = 5.6~\text{m/s} \).
Example:
A tuning fork of frequency \( 512~\text{Hz} \) produces a sound wave. (a) In air, where the speed of sound is \( 340~\text{m/s} \), find the wavelength. (b) In helium, where the speed of sound is \( 1000~\text{m/s} \), find the wavelength. Comment on the frequency.
▶️Answer/Explanation
(a) In air: \( \lambda_{\text{air}} = \dfrac{v}{f} = \dfrac{340}{512} \approx 0.664~\text{m} \).
(b) In helium: \( \lambda_{\text{He}} = \dfrac{v}{f} = \dfrac{1000}{512} \approx 1.953~\text{m} \).
Comment: Frequency \( f \) is set by the source (tuning fork) and remains \( 512~\text{Hz} \) in both media; only \( v \) and \( \lambda \) change with the medium, linked by \( v = f\lambda \).
Transverse Waves
A transverse wave is a type of wave in which the vibration (oscillation) of the particles or field is at right angles (90°) to the direction in which the wave propagates (travels).
Key Features of Transverse Waves:
- Oscillation Direction: Vibrations are perpendicular to wave motion.
- Wave Crest & Trough: Highest points are crests, lowest points are troughs.
- Waveform: Looks like an up-and-down pattern when drawn.
- Wave Speed: As with all waves, given by \( v = f \lambda \).
Everyday Example:
- When you shake one end of a rope up and down, the disturbance moves horizontally along the rope while the rope particles vibrate vertically — a clear transverse wave.
Examples of Transverse Waves
Electromagnetic (EM) Waves:
- Light, radio waves, microwaves, X-rays, gamma rays.
- In EM waves, the electric and magnetic fields oscillate at right angles to the direction of travel.
- No medium is required → they can travel through a vacuum (space).
Water Waves:
- Ripples on a pond are surface transverse waves.
- Water particles move up and down while the wave moves outward horizontally.
- This allows energy to travel across the surface without bulk motion of water.
Seismic S-Waves (Secondary Waves):
- Produced during earthquakes.
- They travel through solids only, not liquids or gases.
- The vibrations of rock particles are perpendicular to the wave’s travel direction.
- Slower than P-waves but cause significant ground shaking.
Example :
A student shakes a slinky up and down to generate a wave. The wave moves horizontally along the floor at \( 2.0~\text{m/s} \). The frequency is \( 5~\text{Hz} \). Find the wavelength.
▶️Answer/Explanation
Using \( v = f\lambda \):
\( \lambda = \dfrac{v}{f} = \dfrac{2.0}{5} = 0.40~\text{m} \).
Final: The wavelength is \( 0.40~\text{m} \).
Longitudinal Waves
A longitudinal wave is a type of wave in which the vibration (oscillation) of the particles is parallel to the direction in which the wave propagates (travels).
Key Features of Longitudinal Waves:
Oscillation Direction: Vibrations are along (parallel to) the same direction as the wave’s motion.
Compressions and Rarefactions:
- Compressions → regions where particles are closer together (high pressure).
- Rarefactions → regions where particles are spread out (low pressure).
Wave Speed: As with all waves, given by \( v = f\lambda \).
Examples of Longitudinal Waves
Sound Waves:
- Produced when vibrating objects (e.g. vocal cords, speakers) create compressions and rarefactions in air.
- The disturbance moves through air (or another medium), but the air particles only vibrate back and forth — they do not travel with the wave.
- Sound cannot travel in a vacuum because there are no particles to compress.
Seismic P-Waves (Primary Waves):
- Generated by earthquakes.
- Fastest seismic waves — they arrive first at detectors.
- Travel through solids, liquids, and gases.
- Cause the ground to oscillate back and forth in the direction of wave travel.
Example:
A loudspeaker produces a sound wave of frequency \( 170~\text{Hz} \). If the speed of sound in air is \( 340~\text{m/s} \), calculate the wavelength of the sound wave.
▶️Answer/Explanation
Using the wave equation: \( v = f\lambda \).
\( \lambda = \dfrac{v}{f} = \dfrac{340}{170} = 2.0~\text{m} \).
Final: The wavelength of the sound wave is \( 2.0~\text{m} \).
Diffraction and the Effect of Wavelength and Gap Size
Diffraction is the bending and spreading of waves when they pass through a narrow gap or around an obstacle. Unlike reflection or refraction, diffraction does not involve a change in the medium the wave continues in the same medium but spreads out more. The degree of diffraction depends on two main factors: the wavelength (\(\lambda\)) of the wave and the size of the gap (a).
Key Principles:
- If \( a \gg \lambda \): The gap is much larger than the wavelength. Diffraction is very small, and the waves continue almost in straight lines with little spreading. The pattern is similar to waves just going through an open door.
- If \( a \approx \lambda \): The gap size is comparable to the wavelength. Strong diffraction occurs, and the waves spread out widely into semicircular wavefronts. This is the condition for maximum noticeable diffraction.
- If \( a \ll \lambda \): The gap is much smaller than the wavelength. Very little of the wave gets through, and the spreading effect is minimal the wave is mostly blocked.
Everyday Examples:
Sound waves: Since sound has a relatively large wavelength (several cm to meters), diffraction is strong. This is why you can hear people talking even if they are behind a wall or around a corner.
Water waves: In a ripple tank experiment, when water waves with \(\lambda \approx a\) pass through a slit, they spread into circular wavefronts. If the slit is much larger than \(\lambda\), only slight spreading is seen.
Light waves: The wavelength of visible light (\(\approx 500 \, \text{nm}\)) is extremely small compared to everyday gaps (like doors or windows). Hence, diffraction is almost unnoticeable in daily life. However, if light passes through a very narrow slit (comparable to its wavelength), diffraction patterns with bright and dark fringes can be observed.
Example:
In a ripple tank, water waves of wavelength \( \lambda = 4.0~\text{cm} \) are incident on a barrier with a gap of width \( a = 5.0~\text{cm} \). Describe the diffraction pattern and explain whether strong diffraction will be observed.
▶️Answer/Explanation
The gap width \( a = 5.0~\text{cm} \) is close to the wavelength \( \lambda = 4.0~\text{cm} \). Since \( a \approx \lambda \), strong diffraction will occur. The waves emerging from the gap will spread widely in semicircular arcs, filling the region behind the barrier.
Example:
A ripple tank produces water waves with a wavelength of \( 2.0~\text{cm} \). The waves approach a barrier with a gap width of \( 2.0~\text{cm} \).
▶️Answer/Explanation
Here, gap width \( a = \lambda = 2.0~\text{cm} \).
This condition gives maximum diffraction, so the waves spread out in semicircular wavefronts after passing through the gap.
If the gap had been much wider (e.g. 10 cm), the waves would hardly spread out at all.