4.2 Sound waves and waves for detection and exploration — Practise

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

Every question on this page is Higher tier. The questions and the answers below come from a set that is checked by computer every time the book is built.

H An ultrasound pulse travels through tissue at 1500 m/s. The reflection returns to the detector after 0.00020 s. Calculate the distance to the boundary.
H A ship uses an echo sounder. A pulse of sound travels through sea water at 1500 m/s and returns from the sea floor after 0.050 s. Calculate the depth of the water.
H An earthquake produces a P-wave that travels 90 km in 15 s. Calculate the speed of the P-wave.
H An ultrasound scanner works at a frequency of 2.5 MHz. The speed of sound in tissue is 1500 m/s. Calculate the wavelength of the ultrasound.
H The upper limit of normal human hearing is 20 kHz. Convert this frequency to hertz.
H The lowest frequency a healthy young person can hear is 20 Hz. Calculate the period of this sound wave.
H In a scan, an ultrasound boundary is 0.060 m from the detector. The speed of sound in tissue is 1500 m/s. Calculate the time for the pulse to travel to the boundary and back.
H Explain why a sound wave cannot travel through a vacuum.
H Explain why the ear can detect sound only over a limited range of frequencies.
H Explain how an ultrasound pulse can be used to find the distance to a boundary inside the body.
H Explain how the study of seismic waves from earthquakes gives evidence about the structure of the Earth, including its core.
H Compare P-waves and S-waves from an earthquake.
H An echo sounder on a boat sends a pulse of sound down through water at 1500 m/s. The reflection returns after 0.080 s. Calculate the depth of the water.

Answers and concise solutions

1. Distance to the boundary

Answer: The pulse travels there and back, so $s = \dfrac{v t}{2} = \dfrac{1500 \times 0.00020}{2} = 0.15\,\text{m}$ . The boundary is 0.15 m away.

2. Depth of the water

Answer: The echo time is for the trip down and back, so the depth is $s = \dfrac{v t}{2} = \dfrac{1500 \times 0.050}{2} = 37.5\,\text{m} = 38\,\text{m}$ to 2 significant figures.

3. Speed of the P-wave

Answer: Convert the distance: $90\,\text{km} = 90000\,\text{m}$ . Then $v = \dfrac{s}{t} = \dfrac{90000}{15} = 6000\,\text{m/s} = 6.0 \times 10^3\,\text{m/s}$ .

4. Wavelength of the ultrasound

Answer: $2.5\,\text{MHz} = 2.5 \times 10^6\,\text{Hz}$ . Then $v = f\lambda$ , so $\lambda = \dfrac{v}{f} = \dfrac{1500}{2.5 \times 10^6} = 6.0 \times 10^{-4}\,\text{m}$ , which is 0.60 mm.

5. Frequency in hertz

Answer: The prefix kilo means one thousand, so $20\,\text{kHz} = 20000\,\text{Hz}$ .

6. Period of the lowest audible sound

Answer: $T = \dfrac{1}{f} = \dfrac{1}{20} = 0.050\,\text{s}$ .

7. Echo time

Answer: The pulse travels twice the distance, so $t = \dfrac{2d}{v} = \dfrac{2 \times 0.060}{1500} = 8.0 \times 10^{-5}\,\text{s}$ .

8. Sound in a vacuum

A sound wave is a longitudinal wave. It travels as a series of compressions and rarefactions, so it needs particles to vibrate.
A vacuum contains no particles, so there is nothing to vibrate and the sound cannot pass through.

9. The range of hearing

Sound waves arriving at the ear make the ear drum and other parts of the ear vibrate. This converts the sound wave into a vibration of a solid.
This conversion only works over a limited range of frequencies, because the parts of the ear cannot vibrate at every frequency.
That limited range sets the limits of human hearing, which is about 20 Hz to 20 kHz.

10. Finding a boundary with ultrasound

When the ultrasound wave meets a boundary between two different materials, part of the wave is reflected back to the detector.
The detector measures the time taken for the reflection to return.
The pulse travelled to the boundary and back, so the distance to the boundary is half of speed x time.

11. Seismic evidence for the Earth

An earthquake produces P-waves, which are longitudinal, and S-waves, which are transverse. P-waves travel at different speeds through solids and liquids.
S-waves cannot travel through a liquid, and they do not pass through the outer core. This shows that part of the core is liquid.
The behaviour of the waves gives evidence about the size and structure of the core, which cannot be seen directly.

12. P-waves and S-waves

A P-wave is a longitudinal wave, so its vibration is along the direction of travel. It can travel through solids and liquids.
An S-wave is a transverse wave, so its vibration is at right angles to the direction of travel. It cannot travel through a liquid.
The two waves travel at different speeds, so they reach a distant detector at different times.

13. Depth of the water

Answer: $s = \dfrac{v t}{2} = \dfrac{1500 \times 0.080}{2} = 60\,\text{m} = 6.0 \times 10^1\,\text{m}$ .