lesson
Link distance per cycle with cycles per second
1 · Learn
Wave speed equals frequency times wavelength: v = fλ. Frequency counts cycles per second and wavelength measures the distance between corresponding points. Amplitude describes maximum displacement in the relevant wave model.
Changing amplitude is not the same as changing frequency. When a wave enters a different medium, its speed and wavelength may change while frequency remains fixed by the source in the usual boundary model.
2 · Worked example
A wave of frequency 5 Hz and wavelength 2 m travels at 10 m/s.
3 · Your turn
Find wavelength for speed 12 m/s and frequency 4 Hz.
Check your answer
3 m.
4 · Apply your learning
Label wavelength and amplitude on an approved diagram and check the equation's units.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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