Lenses and Mirrors Equations Worksheet
Practice with 10 problems on the thin lens equation, mirror equation, magnification, and image formation. Full worked solutions included.
View worksheet →Waves Equations Worksheet
Practice the wave equations with 10 problems covering wave speed, frequency, period, and wavelength. Includes full worked answers.
Equations you will need
| v = fλ | Wave speed = frequency × wavelength |
| T = 1/f | Period = 1 / frequency |
| f = 1/T | Frequency = 1 / period |
Symbol key
| Symbol | Quantity | Unit |
|---|---|---|
| v | wave speed | m/s |
| f | frequency | Hz (hertz) |
| λ | wavelength | m |
| T | period | s |
Practice problems
Attempt each problem on paper first, then click Show answer to check your working.
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A wave has frequency 50 Hz and wavelength 4 m. Find its speed.
Show answer
v = fλ = 50 × 4 = 200 m/s -
A sound wave travels at 340 m/s with wavelength 2 m. Find the frequency.
Show answer
f = v/λ = 340/2 = 170 Hz -
Find the period of a 25 Hz wave.
Show answer
T = 1/f = 1/25 = 0.04 s -
A water wave has a period of 0.5 s and wavelength 1.2 m. Find its speed.
Show answer
f = 1/0.5 = 2 Hz; v = 2 × 1.2 = 2.4 m/s -
Radio waves travel at 3 × 10⁸ m/s. Find the wavelength of a 100 MHz station.
Show answer
λ = v/f = (3×10⁸)/(10⁸) = 3 m -
A wave on a string completes 60 oscillations in 4 s. Find the frequency and period.
Show answer
f = 15 Hz; T = 0.0667 s -
A wave has speed 300 m/s and period 0.01 s. Find the wavelength.
Show answer
f = 100 Hz; λ = 300/100 = 3 m -
Visible red light has wavelength 700 nm. Find its frequency. (c = 3×10⁸ m/s)
Show answer
f = c/λ = 3×10⁸ / 7×10⁻⁷ = 4.29×10¹⁴ Hz -
A wave has frequency 200 Hz and travels 50 m in 0.25 s. Find the wavelength.
Show answer
v = 50/0.25 = 200 m/s; λ = 200/200 = 1 m -
Two waves: A has period 0.02 s, B has period 0.05 s. Which has higher frequency?
Show answer
f_A = 50 Hz; f_B = 20 Hz; A has higher frequency
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About this worksheet
This waves equations worksheet covers the essential equations for waves & optics at the GCSE / A-Level level. Every problem has been written to mirror the style and difficulty of real exam questions, with full algebraic working shown in the solutions.
If you find these problems too straightforward, try the more advanced worksheets in the same topic listed above. If they feel too difficult, start by reviewing the equation definitions in the box at the top of this page and then return to question 1.