How often a wave arrives: period, frequency and wavelength

Question and prediction

Move one end of a rope steadily. When your hand repeats more often, more crests pass each second. Yet crests per second and the distance between crests are different quantities. Before calculating, decide which you would measure with a clock and which with a ruler.

New words without gaps

An oscillation is repeated motion around an equilibrium position. Period T is the time for one complete cycle, measured in seconds. Frequency f is cycles per second, measured in hertz (Hz), so f = 1/T. Wavelength λ is the distance between neighbouring crests at the same instant, measured in metres. Wave speed v is the distance a front travels per second. For a steady wave, v = λf.

Work through supplied data

Supplied example: the hand completes 8 cycles in 4 s. Then f = 8/4 = 2 Hz and T = 4/8 = 0.5 s. If adjacent crests are 1.5 m apart, the front speed is v = 1.5 × 2 = 3 m/s. The diagram marks crests at x = 0, 1.5 and 3 m at one instant. Do not call the crest spacing a period: their units differ.

Test safely

Mark a rope or use the drawing. If you cannot run the activity, label these numbers ‘supplied’. For a real measurement, time many cycles together rather than trying to catch one quick movement with a stopwatch.

A common mistake

The equation v = λf does not mean increasing frequency always increases speed. In a given medium, speed is often set approximately by the medium; wavelength then changes. Keep rope tension fixed when comparing trials.

Support diagram

Transfer to another case

A source completes 6 cycles in 3 s. Find f and T. If speed under the same conditions stays 3 m/s, what is λ? Check your units.

Check your understanding

Close the text and explain the left-to-right drawing to a new learner. Name an observation, a teaching assumption and something the evidence does not prove. Then answer the transfer question without a hint and check units or direction against the diagram. If you disagree, return to the first unfamiliar word rather than memorising a sentence. A spoken explanation, a drawing and a measurement are different kinds of evidence: label each honestly.

Lab notebook page

Add a line to My World Lab Notebook: question → prediction → controlled conditions → changed condition → observation or calculation → conclusion → limit. Put a scale on a drawing or mark it ‘schematic’. If you ran no experiment, write ‘supplied calculation’, not ‘we measured’. Revisit the entry after the next lesson and note what became clearer.

Next lesson: Why does a ruler make sound, and does sound need air?