What are wavefronts?

4 marks · Hard

A wave travels along a stretched string as shown in the figure below.

A sketch of a transverse wave: five complete 'humps' (crests/troughs) shown in a horizontal region of 1.0 m, with the distance from the bottom to the top of a crest labelled 0.12 m.

(a)

Calculate the wavelength of the wave.

[2 marks]

(b)

State the amplitude of the wave.

[1 mark]

(c)

If 20 complete waves pass a point in 4.0 seconds, calculate the frequency.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) Wavelength = 1.0 m / 5 = 0.20 m · must show Correct calculation of number of waves, Correct calculation and value

(b) Amplitude = half the crest-to-trough distance = 0.12 m / 2 = 0.060 m · must show Uses half the vertical distance

Common mistakes: Taking wavelength as distance between peaks, not over number of waves; Using 0.12 m for wavelength not amplitude; Division errors in frequency

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Works out number of waves from diagram (5 waves in 1.0 m)

A1 (a) · 1 mark · Calculates correct wavelength: 0.20 m (or 20 cm, if units clear)

A2 (b) · 1 mark · States amplitude as half the crest-to-trough value (0.06 m)

A3 (c) · 1 mark · Calculates correct frequency (5.0 Hz)

Worked solution

(a) From the diagram, there are 5 complete waves in 1.0 m. Wavelength, .

(b) The amplitude is half the crest-to-trough distance: Amplitude = .