General Properties of Waves
This topic covers the fundamental properties of waves, focusing on how they transfer energy without transferring matter. Understanding wave characteristics and the key equations is essential for solving problems in optics, sound, and electromagnetism.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- Waves are oscillations that transfer energy from one point to another without any net movement of the medium itself.
- In transverse waves, oscillations are perpendicular to the direction of energy transfer (e.g., light, waves on a string). They have peaks and troughs.
- In longitudinal waves, oscillations are parallel to the direction of energy transfer (e.g., sound). They consist of compressions and rarefactions.
- Sound is a mechanical wave and requires a medium (solid, liquid, or gas) to travel through; it cannot travel in a vacuum.
- Electromagnetic (EM) waves are transverse and do not require a medium; they can travel through a vacuum at a speed of 3 x 108 m/s.
Diagram
› Why does this happen?
Why doesn't the medium move along with the wave?
Imagine a 'Mexican wave' in a sports stadium. The wave travels all the way around the stadium, but each person only stands up and sits down in their own seat. They don't run around the stadium with the wave. It's the same for physical waves. The particles of the medium (like water molecules or coils in a spring) are linked by forces to their neighbours. When one particle oscillates, it pulls or pushes on the next one, causing it to oscillate too. This passes the energy of the vibration along the line, but each individual particle just moves back and forth around its fixed position.
Why does sound need a medium to travel?
Sound is a mechanical wave, which means it's caused by the vibration of particles. For sound to travel, particles of a substance (like air, water, or a solid) must knock into their neighbours to pass the vibration along. This creates a chain reaction of compressions (areas where particles are bunched up) and rarefactions (areas where they are spread out). In a vacuum, there are no particles. With nothing to vibrate and knock into each other, there is no way for the sound energy to be transferred from one place to another.
Formulae
f = 1 / T To find the frequency if you know the time period, or vice versa.
v = f × λ This is the core wave equation. Use it to relate wave speed, frequency, and wavelength.
wave speed = distance / time To calculate the speed of a single wave pulse or wavefront travelling a known distance in a specific time.
Definitions
- Amplitude (A)
- The maximum displacement or distance moved by a point on the wave from its equilibrium (rest) position. Units: metres (m).
- Wavelength (λ)
- The distance between two consecutive corresponding points of a wave, such as from one peak to the next peak. Units: metres (m).
- Frequency (f)
- The number of complete waves that pass a fixed point per second. Units: Hertz (Hz), where 1 Hz = 1 wave per second.
- Period (T)
- The time taken for one complete wave to pass a fixed point. Units: seconds (s).
Worked example
A sound wave in air has a frequency of 220 Hz. The distance between the centre of a compression and the centre of the next rarefaction is measured to be 0.75 m. What is the speed of the sound wave?
- 1
Recognise that the distance from a compression to the next rarefaction is half a wavelength (λ/2).
- 2
Calculate the full wavelength:
λ = 2 × 0.75 m = 1.5 m - 3
Identify the given frequency:
f = 220 Hz - 4
Use the wave equation:
v = f × λ - 5
Substitute the values and calculate:
v = 220 Hz × 1.5 m - 6
To calculate 220 × 1.5 mentally:
220 × 1 = 220, and 220 × 0.5 = 110So, v = 220 + 110 = 330 m/s
Answer: 330 m/s
Common mistakes
- ×Mistaking half a wavelength for a full one. The distance between a peak and the next trough (or a compression and the next rarefaction) is λ/2, not λ.
- ×Incorrectly converting between frequency and period, often by multiplying instead of finding the reciprocal.
- ×Arithmetic errors when multiplying or dividing, especially with decimals or large numbers. Always double-check your calculations.
- ×Forgetting the physical constraints of a wave, such as the fact that sound requires a medium and cannot travel in a vacuum.
No-calculator tips
- ✓When calculating `f = 1/T`, convert decimals to fractions first. For example, if T = 0.02 s, that's 2/100 or 1/50 s. The frequency is the reciprocal, so f = 50 Hz.
- ✓To multiply by 1.5, simply add half of the number to itself (e.g., 80 × 1.5 = 80 + 40 = 120). To multiply by 2.5, double the number and add half of the original number (e.g., 40 × 2.5 = 80 + 20 = 100).
- ✓When using the wave equation, estimate the answer first. If f is around 100 Hz and λ is around 3 m, the speed v should be around 300 m/s. This helps to catch major calculation errors.