A speedboat crosses a calm lake, leaving behind a wake of parallel ripples on the water surface. Successive ripple crests are measured to be 80 cm apart, and the ripples are found to travel across the lake at 2.4 m/s. Calculate the frequency of the ripples.

Answer: C. Step 1: Recall the wave equation Wave speed, frequency and wavelength are linked by: v = f Rearranging for frequency: f = v/ Step 2: Convert the wavelength into metres The crest spacing is given in centimetres, so it must be converted to m…

General Wave Properties: Question 6

Syllabus 3.1

Multiple choice Core 1 mark

A speedboat crosses a calm lake, leaving behind a wake of parallel ripples on the water surface. Successive ripple crests are measured to be $80\text{ cm}$ apart, and the ripples are found to travel across the lake at $2.4\text{ m/s}$ . Calculate the frequency of the ripples.

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Step 1: Recall the wave equation

Wave speed, frequency and wavelength are linked by:

$v = f\lambda$

Rearranging for frequency:

$f = \frac{v}{\lambda}$

Step 2: Convert the wavelength into metres

The crest spacing is given in centimetres, so it must be converted to metres before it can be substituted into the formula:

$\lambda = 80\text{ cm} = 0.80\text{ m}$

Step 3: Substitute the values

$f = \frac{2.4\text{ m/s}}{0.80\text{ m}}$

$f = 3.0\text{ Hz}$

Why the other options are wrong

Option	How it arises	Error
$0.030\text{ Hz}$	$2.4 \div 80$	Forgot to convert $80\text{ cm}$ into $0.80\text{ m}$ before dividing
$0.33\text{ Hz}$	$0.80 \div 2.4$	Formula inverted ( $\lambda \div v$ instead of $v \div \lambda$ )
$2.4\text{ Hz}$	reading $v$ as $f$	Quoted the wave speed itself as the frequency, ignoring the wavelength

Final answers

Frequency of the ripples $= \boxed{3.0\text{ Hz}}$ , option C