Waves

Revision notes

Waves transfer energy and information without a net transfer of matter. Transverse oscillations are perpendicular to the direction of energy transfer; longitudinal oscillations are parallel. Important quantities are amplitude, wavelength λ, frequency f and period T. Wave speed is v = fλ and T = \(\dfrac{1}{f}\).

Refraction occurs when wave speed changes at a boundary, usually causing direction to change unless the wave arrives along the normal. Diffraction is spreading when waves pass through a gap or around an obstacle and is strongest when the gap is comparable with the wavelength. All electromagnetic waves travel at the same speed in a vacuum but differ in frequency and wavelength.

Wave quantities and types

A wave transfers energy and information without requiring a net transfer of matter from source to destination. Transverse waves oscillate perpendicular to the direction of energy transfer; longitudinal waves oscillate parallel to it and contain compressions and rarefactions. Frequency is the number of complete oscillations each second and is measured in hertz. Period is the time for one oscillation, so T = \(\dfrac{1}{f}\). Wavelength is the distance between equivalent points on consecutive cycles.

Wave speed is related by v = fλ. Keep units consistent: wavelength in metres, frequency in hertz and speed in metres per second. If the source frequency remains fixed while a wave enters a region where its speed changes, its wavelength must change.

Reflection, refraction and diffraction

For reflection, the angle of incidence equals the angle of reflection, with both angles measured from the normal. Refraction occurs when wave speed changes at a boundary. The frequency is set by the source and remains unchanged; speed and wavelength change. At oblique incidence this usually changes direction. Avoid saying refraction occurs merely because a wave 'hits a boundary'—a speed change is the key idea.

Diffraction is spreading when waves pass through a gap or around an obstacle. It is strongest when the gap size is similar to the wavelength. Longer wavelengths therefore diffract more around a given obstacle or through a given gap.

Sound and electromagnetic waves

Sound is a mechanical longitudinal wave and requires a medium. Its speed depends on the medium and conditions. Electromagnetic waves are transverse and can travel through a vacuum. All electromagnetic waves travel at the same speed in a vacuum but have different frequencies, wavelengths, production mechanisms and interactions with matter.

In order of increasing frequency (decreasing wavelength) the electromagnetic spectrum is: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Higher-frequency radiation carries more energy, and ultraviolet, X-rays and gamma rays are ionising.

Different parts of the spectrum are absorbed, transmitted or reflected differently by materials, which explains these applications.

Practical and graph reasoning

Wave experiments often involve measuring several wavelengths or oscillations to reduce percentage uncertainty. On oscilloscope-style displays, use the time-base scale carefully to determine period before calculating frequency. In ripple-tank or string work, measuring across several cycles is usually more reliable than measuring one.

Exam technique

State what remains constant and what changes. For refraction: frequency constant, speed changes, wavelength changes. For diffraction: discuss wavelength relative to gap size. For wave calculations: write v = fλ, convert centimetres or millimetres to metres, and check that the answer has a sensible magnitude.

Sound and ultrasound

Sound waves are longitudinal and need a medium. They travel faster in solids than in liquids, and faster in liquids than in gases. Humans can hear frequencies from about 20 Hz to 20 kHz.

Ultrasound is separate-physics content. Sound with a frequency above 20 kHz is ultrasound. When ultrasound reaches a boundary between two materials, some is reflected. The time taken for the echo gives the distance to the boundary: distance = speed × time ÷ 2, because the wave travels there and back. Ultrasound is used for medical scanning (for example pre-natal scans) and industrial imaging to find flaws in materials. Echo sounding (sonar) uses high-frequency sound to measure the depth of water.

Worked example: an ultrasound pulse travels at 1500 m/s in water and its echo returns after 0.040 s. Distance = 1500 × 0.040 ÷ 2 = 30 m.

Seismic waves (separate physics)

Earthquakes produce seismic waves. P-waves are longitudinal and can travel through solids and liquids. S-waves are transverse and can travel only through solids. S-waves are not detected on the opposite side of the Earth from an earthquake, which is evidence that the outer core is liquid. P-waves refract at the boundaries inside the Earth, creating shadow zones that show the size of the core.

Black body radiation (separate physics)

All bodies emit and absorb infrared radiation. A perfect black body absorbs all the radiation that falls on it and is also the best possible emitter. The hotter a body is, the more radiation it emits each second and the shorter the wavelength at which the emission peaks. A body at constant temperature absorbs radiation at the same rate as it emits it; it warms up if it absorbs faster than it emits. The temperature of the Earth depends on the balance between the radiation it absorbs and the radiation it emits into space.