Wave Equation & Changing Mediums Revision Notes | GCSE AQA Higher Physics

1. The Universal Wave Language

Every wave in the universe follows the same fundamental rule, whether it's sound bouncing off walls, light travelling through glass, or water ripples spreading across a pond. This rule connects three key properties that determine how waves behave.

Think of waves like a conveyor belt carrying energy. The speed of the belt, how often packages arrive, and the spacing between packages are all connected. Change one property, and the others must adjust to maintain the relationship.

Understanding this connection is crucial for GCSE Physics because it explains everything from why your voice sounds different underwater to how optical fibres carry internet signals around the world.

2. The Wave Equation Revealed

The wave equation is beautifully simple: wave speed equals frequency multiplied by wavelength. Written mathematically, this becomes v = fλ, where v is speed in m/s, f is frequency in Hz, and λ (lambda) is wavelength in m.

Picture a marching band where musicians take steps of different lengths but maintain the same rhythm. If they take longer steps (larger wavelength), they cover more ground per beat (higher speed) whilst keeping the same tempo (frequency).

This equation works for all waves because it describes a fundamental relationship in nature. Sound waves in air, seismic waves in rock, and electromagnetic waves in space all obey this same rule.

The equation can be rearranged to find any unknown quantity. To find frequency: f = v/λ. To find wavelength: λ = v/f. These rearrangements are essential for exam calculations.

3. Calculating with the Wave Equation

Wave equation problems follow a standard pattern in exams. You'll typically be given two quantities and asked to find the third. The key is identifying what you know and what you need to find.

Always start by writing down the wave equation, then substitute the known values with their units. This systematic approach prevents careless errors and shows clear working for method marks.

Worked example: Wave Speed Calculation

A radio wave has frequency 100 MHz and wavelength 3.0 m. Calculate its speed. [3 marks]

1. $v = f\lambda$ — Always start with the correct formula [M1]
2. $f = 100 \text{ MHz} = 100 \times 10^6 \text{ Hz} = 1.0 \times 10^8 \text{ Hz}$ — MHz means million Hz - crucial conversion
3. $v = 1.0 \times 10^8 \times 3.0$ — Include units throughout your working [M1]
4. $v = 3.0 \times 10^8 \text{ m/s}$ — This is the speed of light - makes sense for radio waves [A1]

Answer: 3.0 × 10⁸ m/s

Notice how the answer matches the speed of light. Radio waves are electromagnetic waves, so they travel at light speed in a vacuum. This provides a useful sanity check for your calculation.

4. Waves Changing Medium

When waves travel from one material to another, fascinating changes occur. The frequency always stays the same - it's determined by the source and doesn't change. However, the wave speed and wavelength both change depending on the new medium's properties.

Think of sound travelling from air into water. The source (your voice) still vibrates at the same frequency, but sound travels faster in water than air. Since v = fλ and f is constant, the wavelength must increase to match the higher speed.

This principle explains many everyday phenomena. When light enters glass, it slows down and its wavelength decreases, causing refraction. When seismic waves travel through different rock layers, their speed changes, helping geologists map Earth's interior.

For sound waves specifically, the speed depends on the medium's density and elasticity. Sound travels fastest in solids (around 5000 m/s in steel), slower in liquids (1500 m/s in water), and slowest in gases (340 m/s in air at room temperature).

Worked example: Sound Wave Medium Change

A sound wave has frequency 1000 Hz in air (speed 340 m/s). It enters water where sound travels at 1500 m/s. Calculate the wavelength in both mediums. [4 marks]

1. $\lambda_{air} = \frac{v}{f} = \frac{340}{1000} = 0.34 \text{ m}$ — Using λ = v/f with air values [M1]
2. $f = 1000 \text{ Hz in both mediums}$ — Frequency never changes when crossing boundaries
3. $\lambda_{water} = \frac{v}{f} = \frac{1500}{1000} = 1.5 \text{ m}$ — Same frequency, different speed [M1]
4. Wavelength increases by factor of $\frac{1.5}{0.34} \approx 4.4$ — Wavelength increases when speed increases [A1]

Answer: Air: 0.34 m, Water: 1.5 m

5. Real-World Wave Applications

The wave equation governs countless technologies we use daily. Mobile phones rely on radio waves with specific frequencies and wavelengths to carry signals. GPS satellites transmit waves that travel at light speed, allowing precise distance calculations.

Medical ultrasound uses high-frequency sound waves (typically 2-10 MHz) that reflect off internal organs. The wavelengths are small enough to create detailed images, whilst the frequency determines how deep the waves can penetrate.

Seismologists use the wave equation to locate earthquakes. P-waves and S-waves travel at different speeds through Earth's layers. By measuring arrival times at multiple stations, scientists can triangulate the earthquake's epicentre.

Even musical instruments demonstrate wave principles. A guitar string's length determines the wavelength of standing waves, whilst the tension affects wave speed. Together, these control the frequency we hear as pitch.

6. Exam Success with Wave Calculations

Wave equation questions are common in GCSE Physics papers and follow predictable patterns. Examiners often test unit conversions, so watch for frequencies given in kHz or MHz, and wavelengths in cm or mm.

The most frequent mistake is forgetting to convert units before calculating. Always convert to standard SI units: Hz for frequency, m for wavelength, and m/s for speed. Show this conversion clearly for method marks.

For medium-change questions, remember that frequency is the constant. Students often assume all three quantities change, but frequency is determined by the source and remains fixed. Use this fact to check your answers make sense.