4.1 Waves in air, fluids and solids — Practise

Work through these on your own. Keep your working neat: the method matters as much as the answer.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

A ripple tank makes water waves with a frequency of 4.0 Hz and a wavelength of 0.15 m. Calculate the wave speed.
A sound wave in air has a frequency of 165 Hz. The speed of sound in air is 330 m/s. Calculate the wavelength.
A wave travels along a rope at 12 m/s. The wavelength is 3.0 m. Calculate the frequency.
A sound wave has a frequency of 50 Hz. Calculate its period.
A wave has a period of 0.40 s. Calculate its frequency.
An ultrasound scanner uses a frequency of 2.5 MHz. Convert this frequency to hertz.
A longitudinal wave in a metal bar has a frequency of 1000 Hz and a wavelength of 5.0 m. Calculate the wave speed.
Ten waves pass a point in 4.0 s. Calculate the frequency and the period of the waves.
Describe the difference between a transverse wave and a longitudinal wave. Give one example of each.
A cork floats on water. A water wave passes the cork and the cork bobs up and down but does not move along with the wave. Explain what this shows about what a wave transfers.
Describe a method to measure the speed of sound in air using an echo from a wall.
A water wave travels 24 m in 8.0 s. Calculate the wave speed.

Answers and concise solutions

1. Wave speed of the ripples

Answer: $v = f\lambda = 4.0 \times 0.15 = 0.60\,\text{m/s}$ .

2. Wavelength of the sound wave

Answer: $v = f\lambda$ , so $\lambda = \dfrac{v}{f} = \dfrac{330}{165} = 2.0\,\text{m}$ .

3. Frequency of the wave on the rope

Answer: $v = f\lambda$ , so $f = \dfrac{v}{\lambda} = \dfrac{12}{3.0} = 4.0\,\text{Hz}$ .

4. Period of the sound wave

Answer: $T = \dfrac{1}{f} = \dfrac{1}{50} = 0.020\,\text{s}$ .

5. Frequency of the wave

Answer: $T = \dfrac{1}{f}$ , so $f = \dfrac{1}{T} = \dfrac{1}{0.40} = 2.5\,\text{Hz}$ .

6. Frequency in hertz

Answer: The prefix mega means one million, so $2.5\,\text{MHz} = 2.5 \times 10^6\,\text{Hz} = 2500000\,\text{Hz}$ .

7. Wave speed in the metal bar

Answer: $v = f\lambda = 1000 \times 5.0 = 5000\,\text{m/s} = 5.0 \times 10^3\,\text{m/s}$ .

8. Frequency and period

Answer: $f = \dfrac{10}{4.0} = 2.5\,\text{Hz}$ . The period is $T = \dfrac{1}{f} = \dfrac{1}{2.5} = 0.40\,\text{s}$ .

9. Transverse and longitudinal waves

In a transverse wave the vibration is at right angles to the direction in which the wave travels.
In a longitudinal wave the vibration is along the same line as the direction in which the wave travels, so the wave has areas of compression and rarefaction.
A water ripple is a transverse wave. A sound wave in air is a longitudinal wave.

10. What the cork shows

The cork moves up and down as the wave passes, but it returns to the same place. The water itself does not travel along with the wave.
The wave transfers energy from one place to another, and not water or matter.

11. Measuring the speed of sound

Measure the distance from the sound source to the wall with a tape measure.
Make a short, loud sound and measure the time for the echo to return with a stopwatch or a data logger.
The sound travels to the wall and back, a distance of twice the measured distance. Use v = s / t with this total distance and the measured time.

12. Wave speed

Answer: $v = \dfrac{s}{t} = \dfrac{24}{8.0} = 3.0\,\text{m/s}$ .