Wave speed

Waves

GCSE Physics (8463)

ORIGINAL

Frequency from a count, wavelength in metres, v = fλ — then a new wavelength when only the speed changes.

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Question

Water waves are made in a ripple tank.

12

waves pass a fixed point in

8.0\,\text{s}

, and the distance between neighbouring crests is

40\,\text{cm}

. (a) Calculate the wave speed. (b) The waves pass into shallower water, where they travel at

0.45\,\text{m/s}

. Their frequency does not change. Calculate the new wavelength.

Every step worked, with the reasoning.

1
$f = \dfrac{12}{8.0} = 1.5\,\text{Hz}$
Frequency is the number of waves passing a point each second.
2
$\lambda = 40\,\text{cm} = 0.40\,\text{m}$
The wavelength is the distance from one crest to the next; convert to metres for a speed in m/s.
3
$v = f\lambda = 1.5 \times 0.40 = 0.60\,\text{m/s}$
The wave equation: wave speed = frequency × wavelength.
4
$\lambda_{\text{new}} = \dfrac{v}{f} = \dfrac{0.45}{1.5} = 0.30\,\text{m}$
The frequency is set by the source, so it stays at $1.5\,\text{Hz}$ ; a lower speed means a shorter wavelength.

Answer: (a) $0.60\,\text{m/s}$ ; (b) $0.30\,\text{m}$ ( $30\,\text{cm}$ )