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    Wave speed calculations: worked examples

    By Engr. Mehmood Kakar · Updated

    Quick answer

    Use v = fλ: wave speed = frequency × wavelength. Convert frequency to hertz and wavelength to metres first (MHz × 10⁶, nm × 10⁻⁹, cm ÷ 100). If you are given the period instead of the frequency, use f = 1 ÷ T. For echoes, remember the sound travels there and back.

    The two wave equations

    Almost every wave calculation at GCSE uses one or both of these:

    • v = f λ: wave speed (m/s) = frequency (Hz) × wavelength (m)
    • T = 1 ÷ f: period (s) = 1 ÷ frequency (Hz)

    Both are on the equation sheet. The marks are in converting units and choosing the right one.

    Sound waves

    A sound wave in water has a speed of 1500 m/s and a frequency of 3000 Hz. Calculate its wavelength. (3 marks)

    1. λ = v ÷ f
    2. λ = 1500 ÷ 3000
    3. λ = 0.50 m

    Light and standard form

    Green light has a frequency of 6.0 × 10¹⁴ Hz. The speed of light is 3.0 × 10⁸ m/s. Calculate its wavelength in nanometres. (3 marks)

    1. λ = v ÷ f = 3.0 × 10⁸ ÷ 6.0 × 10¹⁴
    2. λ = 5.0 × 10⁻⁷ m
    3. 1 nm = 10⁻⁹ m, so λ = 5.0 × 10⁻⁷ ÷ 10⁻⁹
    4. λ = 500 nm

    Type standard form on your calculator using the ×10ˣ (or EXP) button, not by typing "× 10 ^". It avoids bracket mistakes.

    Ripple tank measurements

    In the waves required practical, you measure frequency and wavelength, then calculate speed.

    In a ripple tank, 10 waves pass a point in 5.0 s. The wavelength is 3.0 cm. Calculate the wave speed. (4 marks)

    1. Frequency: f = 10 ÷ 5.0 = 2.0 Hz
    2. Convert: λ = 3.0 cm = 0.030 m
    3. v = f × λ = 2.0 × 0.030
    4. v = 0.060 m/s

    The period here is T = 1 ÷ 2.0 = 0.50 s: each wave takes half a second to pass.

    Echoes

    A student claps and hears the echo from a wall 0.50 s later. Sound travels at 340 m/s. How far away is the wall? (3 marks)

    1. Total distance: s = v × t = 340 × 0.50 = 170 m
    2. That is there and back, so halve it
    3. Distance to wall = 85 m

    Practice

    1. A tuning fork produces a 512 Hz sound with a wavelength of 0.66 m. Calculate the speed of sound.

    v = 512 × 0.66 = 337.92 → v = 338 m/s

    2. A radio wave has a wavelength of 1500 m. Calculate its frequency in kHz. (v = 3.0 × 10⁸ m/s)

    f = 3.0 × 10⁸ ÷ 1500 = 200,000 Hz → f = 200 kHz

    3. A wave has a period of 0.004 s. Calculate its frequency.

    f = 1 ÷ 0.004 → f = 250 Hz

    Frequently asked questions

    How do you calculate wave speed?

    Multiply the frequency in hertz by the wavelength in metres: v = fλ. For example, 50 Hz × 6.8 m = 340 m/s.

    How do you measure the speed of water waves in a ripple tank?

    Count how many waves pass a point in a measured time to find the frequency, measure the wavelength using a ruler against the projected waves, then use v = fλ.

    Why do you halve the distance in echo questions?

    The sound travels to the wall and back, so the total distance is twice the distance to the wall.

    Do all waves travel at the same speed?

    No. All electromagnetic waves travel at the same speed in a vacuum (about 3.0 × 10⁸ m/s), but sound and water waves are much slower and depend on the material they travel through.

    Engr. Mehmood Kakar

    Written by Engr. Mehmood Kakar

    Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)

    Checked against the AQA GCSE Physics (8463) specification on 14 November 2026.