Wave questions often contain three related quantities that answer different questions. Frequency counts cycles per second, period measures time per cycle, and wavelength measures the spatial separation of matching phases. Begin by identifying which quantity the problem gives.
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Translate the description into quantities
Consider an ideal periodic travelling wave with frequency f = 50 Hz and speed v = 120 m/s in a uniform medium. A fixed point experiences 50 complete cycles each second. The time for one cycle is T = 1/f = 0.020 s.
The wavelength is given by v = fλ, so λ = 120/50 = 2.4 m. The period is a time and the wavelength is a distance. Giving both answers in metres would reveal a conceptual error.
Use the units as a check
A hertz is one cycle per second. Dividing metres per second by cycles per second leaves metres per cycle, which corresponds to a wavelength. Multiplying frequency by period gives one: fT = 1.
The numbers also tell a consistent story. During one period, the wave pattern moves vT = 120 × 0.020 = 2.4 m, exactly one wavelength.
Reason about a change of medium
For transmission across a stationary boundary driven by the same source, the frequency remains the source frequency. If the transmitted wave speed is 80 m/s, its wavelength is 80/50 = 1.6 m. Its period remains 0.020 s.
This example assumes a suitable transmitted periodic wave and a stationary boundary. It does not determine the amplitude, reflected fraction or energy transfer from wave speed alone.
Avoid a common shortcut
It is tempting to say that a faster wave must have a higher frequency. That conclusion requires an additional condition, such as a fixed wavelength. With a fixed source frequency, a higher speed instead means a longer wavelength.
For each practice problem, write the fixed quantity before applying the equation. Then check whether the answer describes a time, distance or speed. This is an original foundation exercise, not an official Olympiad question; current activity details should be checked through the relevant organisers.
Continue reading: British Physics Olympiad Mechanics: Momentum vs Kinetic Energy.
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Official information and further reading: Source 1
