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    Wave Speed Calculator (v = fλ)

    GCSE PhysicsAQAEdexcelOCRFoundation & Higher

    Find wave speed, frequency or wavelength using v = f × λ. Works for sound, water and electromagnetic waves, with MHz and nm conversions done for you.

    Quick answer

    Wave speed = frequency × wavelength. Use hertz and metres to get m/s. For example, a 50 Hz sound wave with a wavelength of 6.8 m travels at 50 × 6.8 = 340 m/s. Convert MHz and nm to Hz and m first.

    By Engr. Mehmood Kakar · Updated

    v = f × λ
    Find:

    Simulation

    See v = fλ happen

    Change the frequency and the wavelength. The highlighted crest moves at the wave speed, while the marked particle only moves up and down.

    0.5 Hz
    2 m

    The wave transfers energy, not the medium: the marked particle stays in the same place horizontally.

    Put these numbers in the calculator above

    How to calculate wave speed

    Every wave, from ripples on a pond to radio waves, obeys the same equation linking its speed, frequency and wavelength:

    wave speed = frequency × wavelength

    • v is wave speed in metres per second (m/s)
    • f is frequency in hertz (Hz): waves per second
    • λ (lambda) is wavelength in metres (m)

    A sound wave with a frequency of 50 Hz and a wavelength of 6.8 m travels at 50 × 6.8 = 340 m/s.

    Prefixes are where marks go. Radio frequencies are often in MHz (× 1 000 000) and light wavelengths in nanometres (× 10⁻⁹). All electromagnetic waves travel at the same speed in a vacuum, about 3.0 × 10⁸ m/s, so a higher frequency always means a shorter wavelength.

    Wave speed is the speed at which energy is transferred, not the speed of the water or air itself, which only oscillates back and forth.

    Common mistakes that cost marks

    1. Not converting MHz or kHz. 100 MHz is 100 000 000 Hz.
    2. Leaving wavelength in cm or nm. 40 cm is 0.40 m; 500 nm is 5.0 × 10⁻⁷ m.
    3. Mixing up frequency and period. Frequency is waves per second; period is seconds per wave (T = 1/f).
    4. Rearranging the wrong way. λ = v ÷ f. A higher frequency gives a shorter wavelength.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A sound wave has a frequency of 50 Hz and a wavelength of 6.8 m. Calculate its speed.[2 marks]
    1. v = f × λ
    2. v = 50 × 6.8
    3. v = 340 m/s
    Q2A radio wave travels at 3.0 × 10⁸ m/s with a frequency of 100 MHz. Calculate its wavelength.[3 marks]
    1. Rearrange: λ = v ÷ f
    2. Convert: f = 100 × 1 000 000 = 1.0 × 10⁸ Hz
    3. λ = 3.0 × 10⁸ ÷ 1.0 × 10⁸
    4. λ = 3.0 m
    Q3Water waves travel at 1.2 m/s and have a wavelength of 40 cm. Calculate their frequency.[3 marks]
    1. Rearrange: f = v ÷ λ
    2. Convert: λ = 40 ÷ 100 = 0.40 m
    3. f = 1.2 ÷ 0.40
    4. f = 3.0 Hz

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is the equation for wave speed?

    Wave speed = frequency × wavelength (v = fλ). Speed is in m/s, frequency in hertz (Hz) and wavelength in metres (m).

    What is the speed of electromagnetic waves?

    All electromagnetic waves travel at the same speed in a vacuum, about 3.0 × 10⁸ m/s.

    What happens to wavelength if frequency increases?

    At a constant speed, wavelength decreases. Doubling the frequency halves the wavelength.

    What is 1 hertz?

    One wave (or oscillation) per second.