Waves, Sound and the Electromagnetic Spectrum

What you need to know

• A wave is a disturbance that transfers energy from one point to another without any permanent transfer of the medium itself. The water molecules in a pond move up and down as a ripple passes; they do not travel across the pond with it.
• In a transverse wave the particles vibrate at right angles to the direction of travel: water waves, light and all electromagnetic waves, and waves on a stretched string. These have crests and troughs and can be polarised.
• In a longitudinal wave the particles vibrate along the direction of travel: sound waves and waves in a stretched spring pushed end-on. These have compressions and rarefactions and cannot be polarised.
• Mechanical waves such as sound and water waves need a material medium, which is why sound cannot travel through a vacuum. Electromagnetic waves need no medium and travel through a vacuum at 3.0 x 10^8 m/s.
• Wavelength is the distance between two successive points in phase, such as crest to crest. Amplitude is the maximum displacement from the rest position and determines loudness in sound and brightness in light. Frequency is the number of complete waves per second in hertz, and period T = 1/f.
• The universal wave equation is v = f lambda. Distance between a crest and the nearest trough is half a wavelength; distance between a compression and the nearest rarefaction is also half a wavelength.
• Sound is produced by a vibrating body, travels as a longitudinal pressure wave, and moves at about 330 to 340 m/s in air. Its speed increases with temperature and is much greater in liquids and solids than in air, roughly 1500 m/s in water and 5000 m/s in steel.
• An echo is sound reflected from a hard surface. The reflecting surface must be far enough away that the echo arrives after the original sound has died out: distance d is found from 2d = v t, because the sound makes a round trip.
• Pitch depends on frequency, loudness depends on amplitude, and quality or timbre depends on the number and strength of overtones present. That is why a flute and a trumpet playing the same note at the same loudness still sound different.
• The audible range for a healthy human ear is about 20 Hz to 20 000 Hz. Below 20 Hz is infrasound; above 20 000 Hz is ultrasound, used in echo sounding to measure sea depth, in sterilising, in metal flaw detection and in medical scanning.
• In a closed pipe only odd harmonics are present and the fundamental frequency is f = v/(4L); in an open pipe all harmonics are present and the fundamental is f = v/(2L). A closed pipe therefore sounds an octave lower than an open pipe of the same length.
• For a stretched string, the fundamental frequency f = (1/(2L)) sqrt(T/mu), where T is the tension and mu the mass per unit length. Frequency rises when you shorten the string, tighten it, or use a lighter string, which is precisely how a guitar is tuned and fingered.
• The electromagnetic spectrum in order of increasing frequency (decreasing wavelength) is radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. All travel at 3.0 x 10^8 m/s in a vacuum and all are transverse.
• Uses to know: radio waves for broadcasting, microwaves for satellite communication, radar and cooking, infrared for remote controls and thermal imaging, ultraviolet for sterilisation and detecting forged notes, X-rays for imaging bones and checking welds, gamma rays for sterilising equipment and treating cancer. The high-frequency end ionises tissue and is dangerous in large doses.