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 = \(\dfrac{1}{f}\).

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.

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.

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.