In one second, f waves leave the source, each one λ long. So the front of the wave has moved f × λ metres in that second.

wave speed = frequency × wavelength
v = f λ

v in m/s, f in Hz, λ in metres. Recall this one for every board. Rearranged: f = v ÷ λ and λ = v ÷ f.

1. A dolphin call: 6 kHz in sea water at 1500 m/s
2. 6 kHz = 6000 Hz
3. λ = v ÷ f = 1500 ÷ 6000 = 0.25 m
4. 0.25 m = 25 cm

Change every quantity into base units (Hz, m, s) before it goes into the equation.

• k (kilo) = 10³, M (mega) = 10⁶, G (giga) = 10⁹
• c (centi) = 10⁻², m (milli) = 10⁻³, μ (micro) = 10⁻⁶, n (nano) = 10⁻⁹

1. Light: λ = 600 nm = 600 × 10⁻⁹ m = 6.00 × 10⁻⁷ m
2. f = v ÷ λ = 3.00 × 10⁸ ÷ 6.00 × 10⁻⁷
3. f = 5.00 × 10¹⁴ Hz

On a calculator, type standard form with the ×10ˣ (EXP) key, not "× 10 ^", or brackets go wrong.

Ripple tank. A lamp above the tank throws the ripples' shadows onto paper below.

• Wavelength: lay a ruler beside the shadows (or photograph them) and measure across 10 waves, then divide by 10. One wave is too small to measure well.
• Frequency: count the waves passing a mark in 10 s and divide by 10 (or read the setting on the signal generator).
• Speed: v = f λ.

Waves on a string. A vibration generator shakes a string that runs over a pulley to hanging masses. Adjust the frequency until the string shows a steady pattern of loops.

• Each loop is half a wavelength: measure across all the loops, divide by the number of loops, and double it.
• Read f from the signal generator, then v = f λ. The hanging mass (the tension) and the string are control variables.

At a fixed tension, a higher frequency gives a shorter wavelength, but f × λ, the speed, stays the same.