Waves — Natural Physical Science (General Science, age 15)

Sub-strand goals (Specific Learning Outcomes):

• a) Explain the terms used in waves.
• b) Interpret the wave equation as used in science.
• c) Calculate wave characteristics using the wave equation.
• d) Demonstrate the effects of properties of waves in real life.
• e) Appreciate the applications of waves in everyday life.

1. What is a wave?

A wave is a disturbance that transfers energy (and sometimes information) from one place to another without transporting matter permanently. Waves occur in water, sound, light, seismic activity and many man-made technologies (radio, phones, medical ultrasound).

Types of waves

• Transverse waves: the particles of the medium move perpendicular to the direction of wave travel (e.g., waves on a rope, light).
• Longitudinal waves: the particles move parallel to the direction of wave travel (e.g., sound in air, compression waves in a slinky).
• Mechanical waves: need a medium (water waves, sound).
• Electromagnetic waves: do not need a medium (light, radio, X-rays).

Key terms (with simple definitions)

• Crest: highest point of a transverse wave.
• Trough: lowest point of a transverse wave.
• Amplitude (A): maximum displacement from the rest (equilibrium) position; related to energy.
• Wavelength (λ, lambda): distance between successive identical points on a wave (e.g., crest to crest).
• Frequency (f): number of complete waves passing a point each second (measured in hertz, Hz).
• Period (T): time taken for one complete wave to pass (T = 1/f).
• Wave speed (v): speed at which the wave travels through a medium.
• Compression / Rarefaction: in a longitudinal wave, compressions are where particles are close; rarefactions where they are spread out.

2. The wave equation and interpretation

The basic wave equation links speed (v), frequency (f) and wavelength (λ):

v = f × λ

Units: v in metres per second (m/s), f in hertz (Hz), λ in metres (m). Interpretation:

• For a given wave speed, higher frequency means shorter wavelength.
• For a given frequency, a longer wavelength means higher speed (in the same medium).
• Period T = 1/f, so v = λ / T as an alternative form.

Worked examples

3. Calculations & practice problems (with answers)

1. Calculate the frequency of a wave with speed 12 m/s and wavelength 3 m. (Answer: f = v/λ = 12/3 = 4 Hz.)
2. A water wave has period 0.5 s and wavelength 1.2 m. Find its speed. (Answer: v = λ/T = 1.2/0.5 = 2.4 m/s.)
3. Ultrasound used in a clinic has frequency 2 MHz (2 × 10^6 Hz). If speed in body tissue ≈ 1500 m/s, what is λ? (Answer: λ ≈ 1500 / 2×10^6 = 7.5×10^-4 m = 0.75 mm.)

4. Properties of waves and real-life effects

Key properties and simple Kenyan-context examples:

• Reflection: Echo from cliffs at the shores of Lake Victoria; echoes used in sonar and measuring distance.
• Refraction: Bending of light when fishing with a spear — the fish appears at a different position because light bends at the water surface.
• Diffraction: Sound from a market travels around buildings — low-frequency sound diffracts more widely.
• Interference: When two waves meet, they can add (constructive) or cancel (destructive) — seen as patterns on a pond if two stones are dropped.
• Absorption: Materials can reduce wave energy — walls absorb radio or sound, affecting phone signal or classroom acoustics.
• Polarization: Light waves can be filtered by polarizing sunglasses to reduce glare from bright surfaces (e.g., road or water).

Simple classroom demonstrations & suggested learning experiences

• Transverse wave on a rope: One pupil holds one end, teacher quickly moves the other end up and down to create crests and troughs. Measure wavelength by marking two consecutive crests along the rope; measure time for fixed number of pulses to find frequency.
• Longitudinal wave with slinky: Push and pull the slinky to show compressions and rarefactions. Compare speed of pulses by timing movement along the slinky.
• Water ripple tank (or tray): Drop a pebble and watch circular waves, interference when two pebbles are dropped. Use a ruler to measure wavelength and calculate speed if you can time waves.
• Sound and smartphone app: Use a free frequency meter app to measure sound frequency from a tuning fork or whistle; relate to wavelength using speed of sound (≈340 m/s).
• Echo experiment (outdoor): Clap near a large wall or cliff and measure time between sound and echo. Distance to wall = (v × time) / 2. Discuss safety and quiet location.
• Refraction demo: Place a pencil in a glass of water and observe apparent bending. Discuss light speed change between air and water.

5. Real-life applications (why waves matter)

• Communication: radio, TV, mobile phones use electromagnetic waves to carry signals across Kenya and the world.
• Medical imaging: ultrasound uses sound waves to visualize babies and internal organs.
• Navigation & fishing: sonar uses sound waves to find fish and measure depth in lakes like Victoria.
• Engineering: understanding seismic waves helps interpret earthquakes along the East African Rift and design safer buildings.
• Everyday life: microwaves heat food, light allows vision, and sound enables speech and music.

6. Classwork and assessment ideas

1. Short answer: Define amplitude, wavelength, frequency, period and wave speed with units.
2. Calculation: A radio wave has frequency 1000 kHz. If it travels at speed of light (3.0×10^8 m/s), find its wavelength. (Answer: λ = c/f = 3.0×10^8 / 1.0×10^6 = 300 m.)
3. Practical: Measure the speed of a pulse on a rope. Describe method, results and sources of error.
4. Explain: Give two examples of wave reflection and two of refraction from daily life in Kenya.

7. Safety & practical tips

• Do practicals in a clear area to avoid tripping on ropes and slinkies.
• When doing echo experiments, choose quiet spaces and avoid disturbing neighbours.
• When using electronic devices (apps) for sound, keep volumes safe for hearing.