Waves and sound
What a wave is, how wavelength, frequency and speed fit together, how sound travels, how waves add up, why strings and pipes ring at set notes, and the electromagnetic spectrum. The wave lab draws ropes, springs, sound in a tube, ripple tanks and standing waves from the same formulas used in the lessons.
About this course
A wave carries energy without carrying the material along. On a rope, one piece moves up and down while the wave moves right, at right angles to the direction of travel. In a spring, the coils move along the direction of travel and bunch into compressions. The course builds from that picture to wavelength, frequency and speed, which fit together as v = fλ. In the wave lab a rope 6 m long carries a wave, and if you double f, the wavelength has to halve to keep the speed fixed.
The six units are what a wave is, wavelength, frequency and speed, sound, interference and diffraction, standing waves and musical instruments, and the electromagnetic spectrum. Sound goes faster in liquids and solids than in air because they are much harder to compress. If you clap in front of a cliff and hear the echo 2.0 s later, with sound at 343 m/s, you can work out how far away it is. Noise-cancelling headphones listen to the incoming noise and play a wave with its highs and lows reversed. OpenStax 27.3 notes that Young's double slit experiment of 1801 led to acceptance of the wave character of light. The lab draws ropes, springs, sound in a tube, ripple tanks and standing waves from the same formulas used in the lessons.
The last unit puts numbers on the spectrum. A microwave oven runs at 2.45 GHz, so its waves are about 12 cm long, and red laser light at 633 nm is about 190 000 times shorter. A higher frequency means more energy per photon, but penetration depends on the material and wavelength. X-rays can pass through soft tissue, while UV absorbed by skin can damage it.
Before you start
Most of this course comes back to one relation: speed equals frequency times wavelength. If you can rearrange a simple formula, as practised in Linear equations, you are ready. The last unit uses powers of ten for radio and light waves, so scientific notation is worth a quick review.
When you finish
You will be able to find amplitude, period and wave speed from a sketch, estimate how far away lightning struck from the gap before thunder, and explain why astronauts cannot hear a shout in space. You can also predict what happens when crest meets trough, work out the wavelength of a 100 MHz FM signal, and say why a pipe or string rings at set notes.
- 1What is a wave?Far from shore a gull rides up and down as each wave passes, yet it does not travel with the wave.
- 2Wavelength, frequency and speedOcean crests 10 m apart that lift a gull once every 5 s are moving at 2 m/s.
- 3SoundSound covers about 343 metres each second in air at 20 °C, so thunder 3 seconds after a flash means the lightning was about 1 km away.
- 4Interference and diffractionNoise-cancelling headphones make a second sound that is the exact opposite of the noise, and the two add up to near silence.
- 5Standing waves and musical instrumentsA tube closed at one end and 67.2 cm long sounds 128 Hz on a 22 °C day, a little below the C under middle C (130.8 Hz).
- 6The electromagnetic spectrumA microwave oven runs at 2.45 GHz, so its waves are about 12 cm long; red laser light is 633 nm, about 190 000 times shorter.
Sources for this course (11)
- OpenStax College Physics 2e (openstax.org/books/college-physics-2e): 16.9 Waves (disturbance that propagates, gull example λ 10.0 m, T 5.00 s, v = 2.00 m/s, transverse and longitudinal, amplitude independent of speed)
- 16.10 Superposition and Interference (constructive, destructive, standing waves, f1 = v/2L, beats fB = |f1 − f2|, 256 Hz fork with 2 beats -> 254 or 258 Hz)
- 17.2 Speed of Sound (Table 17.1: air 331 m/s at 0 °C, helium 965, fresh water 1480, sea water 1540, steel 5960, vulcanized rubber 54; v = 331 m/s × √(T/273 K); 343 m/s at 20 °C; audible range 20 to 20 000 Hz; P-waves 4 to 7 km/s, S-waves 2 to 5 km/s; Oldham and Lehmann)
- 17.3 Sound Intensity (I0 = 10⁻¹² W/m², Table 17.2, factor 10 = 10 dB, factor 2 = 3 dB, 85 dB for 8 h footnote, bel named for Bell)
- 17.5 Sound Interference and Resonance (noise-cancelling headphones 30 dB or more, closed tube λ = 4L and f_n = n v/4L with n odd, open tube f_n = n v/2L, 128 Hz tube at 22 °C = 0.672 m, ninth harmonic 1.15 kHz, trumpet vs clarinet overtones)
- 24.1 (Maxwell; Hertz from 1887)
- 24.3 The Electromagnetic Spectrum (c = fλ, Table 24.1, three rules of thumb, AM 540 to 1600 kHz, FM 88 to 108 MHz, microwave oven 2.45 GHz, visible 400 to 750 nm, UV 400 to about 10 nm, UV-A 320 to 400, UV-B 290 to 320, UV-C 220 to 290 nm, 99% of surface UV is UV-A, X-rays below 0.01 nm)
- 27.3 Young's Double Slit (1801, d sin θ = mλ, 0.0100 mm and 633 nm example)
- NASA science.nasa.gov/ems (Introduction, Visible Light: 380 to 700 nm; atmospheric windows)
- NIST, c = 299 792 458 m/s exact (nist.gov/si-redefinition/meter)
- ISO 16:1975 (A = 440 Hz, iso.org/standard/3601.html).
Checked: 2026-10-17