The wave equation and wave properties explained

• Amplitude: the maximum displacement from the rest position.
• Wavelength (λ): the distance from one point on a wave to the same point on the next, e.g. crest to crest.
• Frequency (f): the number of waves passing a point each second, in hertz (Hz).
• Period (T): the time for one wave: $T = \dfrac{1}{f}$.

1. A wave has a frequency of 200 Hz and a wavelength of 1.7 m. $v = 200 \times 1.7 = 340$ m/s.
2. Microwaves have a frequency of 2.4 GHz. $\lambda = 3 \times 10^8 \div (2.4 \times 10^9) = 0.125$ m (12.5 cm).
3. A wave has a period of 0.05 s. $f = 1 \div 0.05 = 20$ Hz.

A student claps in front of a wall and hears the echo 0.5 s later. Sound travels at about 340 m/s, so in 0.5 s it travels $340 \times 0.5 = 170$ m. That's there and back, so the wall is $170 \div 2 = 85$ m away. Forgetting to halve is the classic mistake.

In order of increasing frequency (and decreasing wavelength): radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. All travel at $3 \times 10^8$ m/s in a vacuum. Higher-frequency radiation carries more energy per wave, which is why ultraviolet, X-rays and gamma rays can be harmful to cells.

• Confusing amplitude with wavelength.
• Not converting kHz, MHz or GHz to Hz.
• Forgetting the "there and back" in echo questions.

• Reflection: a wave bounces off a surface. For light, the angle of incidence equals the angle of reflection.
• Refraction: a wave changes speed when it enters a different medium, and changes direction unless it enters along the normal. Light slows down entering glass and bends towards the normal.
• Diffraction: a wave spreads out as it passes through a gap or round an edge. It spreads most when the gap is about the same size as the wavelength, which is why you can hear round corners but not see round them.

1. A water wave has a frequency of 2 Hz and a wavelength of 1.5 m. What is its speed?
2. A sound of frequency 680 Hz travels at 340 m/s. What is its wavelength?
3. A wave has a period of 0.01 s. What is its frequency?

Answers: 3 m/s; 0.5 m; 100 Hz.