4.1 Waves in air, fluids and solids — Practise with help

Work each problem first. Open a hint only if you are stuck, and the full working only to check.

Warm-up: remember

A runner covers 400 m in 50 s. Calculate her average speed.
A train travels 900 m at a steady speed of 25 m/s. Calculate the time taken.

Answers

$v = \dfrac{s}{t} = \dfrac{400}{50} = 8.0\,\text{m/s}$ .
$t = \dfrac{s}{v} = \dfrac{900}{25} = 36\,\text{s}$ .

If question 1 went wrong, look again at Section 3.1: average speed is the total distance divided by the total time. If question 2 went wrong, rearrange $v = \dfrac{s}{t}$ to make $t$ the subject first.

Practise with help

1. A water wave has a frequency of 2.0 Hz and a wavelength of 0.30 m. Calculate the wave speed.

Hint

The wave speed is the frequency multiplied by the wavelength.

Next step

Write $v = f\lambda$ , then put in $f = 2.0$ and $\lambda = 0.30$ .

Full working

\begin{aligned} v &= f \lambda \\ &= 2.0 \times 0.30 \\ &= 0.60\,\text{m/s} \end{aligned}

2. A sound wave in air has a frequency of 155 Hz. The speed of sound in air is 310 m/s. Calculate the wavelength.

Hint

You are looking for the wavelength, so the wave equation needs rearranging.

Next step

Start from $v = f\lambda$ and divide both sides by $f$ , so $\lambda = \dfrac{v}{f}$ . Then divide 310 by 155.

Full working

\begin{aligned} v &= f \lambda \\ \lambda &= \frac{v}{f} \\ &= \frac{310}{155} \\ &= 2.0\,\text{m} \end{aligned}

3. A wave travels along a rope at 15 m/s. The wavelength is 3.0 m. Calculate the frequency.

Hint

Frequency is the number of waves each second. Use the wave equation and make $f$ the subject.

Next step

Rearrange $v = f\lambda$ to $f = \dfrac{v}{\lambda}$ , then divide 15 by 3.0.

Full working

\begin{aligned} v &= f \lambda \\ f &= \frac{v}{\lambda} \\ &= \frac{15}{3.0} \\ &= 5.0\,\text{Hz} \end{aligned}

4. A wave has a frequency of 2.0 Hz. Calculate its period.

Hint

The period is the time for one wave, so it is the reciprocal of the frequency.

Next step

Write $T = \dfrac{1}{f}$ , then work out $\dfrac{1}{2.0}$ .

Full working

\begin{aligned} T &= \frac{1}{f} \\ &= \frac{1}{2.0} \\ &= 0.50\,\text{s} \end{aligned}

5. A wave travels at 1200 m/s with a frequency of 400 Hz. Calculate the wavelength.

Hint

The wavelength is the distance the wave travels in the time for one wave.

Next step

Use $\lambda = \dfrac{v}{f}$ , then divide 1200 by 400.

Full working

\begin{aligned} \lambda &= \frac{v}{f} \\ &= \frac{1200}{400} \\ &= 3.0\,\text{m} \end{aligned}

6. Twenty waves pass a point in 5.0 s. Calculate the frequency of the waves.

Hint

Frequency is the number of waves in one second, so divide the number of waves by the time in seconds.

Next step

Work out $\dfrac{20}{5.0}$ . The unit is waves per second, or hertz.

Full working

\begin{aligned} f &= \frac{\text{number of waves}}{\text{time}} \\ &= \frac{20}{5.0} \\ &= 4.0\,\text{Hz} \end{aligned}

The period would be $T = \dfrac{1}{4.0} = 0.25\,\text{s}$ .

7. A cork floats on a pond. A water wave passes the cork, and the cork moves up and down but stays in the same place. Explain what this shows about what the wave transfers.

Hint

Compare what the cork does with what the wave does. The wave moves across the pond, but does the water?

Next step

Say that the water moves up and down and returns to its place, then say what does travel across the pond.

Full working

The cork bobs up and down as each ripple passes, but it always returns to the same place. The water itself does not travel across the pond. The ripple is the wave, and it carries energy from one place to another. So the wave transfers energy without transferring the medium. This answer is a model answer for you to compare with your own wording.