P24: Sound and Ultrasound
Sound waves as longitudinal waves, the speed of sound in different media, and applications of ultrasound and infrasound in medicine and industry.
Sound Waves
Sound waves are longitudinal waves produced by vibrating objects. They require a medium to travel through and cannot travel through a vacuum.
- Sound is produced by vibrating sources such as vocal cords, speaker cones and tuning forks
- Sound travels as a series of compressions (high pressure regions) and rarefactions (low pressure regions)
- The vibrations are passed from particle to particle through the medium
- Sound travels fastest in solids, slower in liquids and slowest in gases
The frequency of a sound wave determines its pitch. Higher frequency means higher pitch. The amplitude of a sound wave determines its volume. Larger amplitude means louder sound.
Speed of Sound
The speed of sound depends on the medium it travels through. Sound travels faster in denser materials because particles are closer together, allowing vibrations to pass more quickly.
| Medium | Approximate Speed | Reason |
|---|---|---|
| Air (20 °C) | 343 m/s | Particles far apart — slower transfer of vibrations |
| Water | 1500 m/s | Particles closer together — faster transfer |
| Steel | 5000 m/s | Particles very close — rapid transfer |
Sound also travels faster in warmer conditions because particles have more kinetic energy and vibrate more quickly, passing on the disturbance faster.
Measuring the Speed of Sound
Method 1: Echo Method
- Stand a measured distance (e.g. 100 m) from a large, flat wall
- Make a loud sound (e.g. clap two wooden blocks together)
- Start a stopwatch when you see the clap and stop it when you hear the echo
- Speed = 2 × distance / time (multiply by 2 because sound travels there and back)
- To improve accuracy, measure the time for several claps and divide
Method 2: Two Microphones and an Oscilloscope
- Place two microphones a known distance apart connected to an oscilloscope
- Produce a sound near the first microphone
- Measure the time difference between the two signals on the oscilloscope display
- Speed = distance between microphones / time difference
When using the echo method, remember the sound travels to the wall AND back, so you must double the distance or halve the total time to find the one-way distance.
Hearing Range
The human hearing range is approximately 20 Hz to 20,000 Hz. Sound below 20 Hz is called infrasound. Sound above 20,000 Hz is called ultrasound.
- Human hearing deteriorates with age, especially the upper frequency limit
- Dogs can hear up to about 45,000 Hz
- Bats and dolphins use ultrasound for echolocation
- The ear converts sound waves into electrical signals that the brain interprets
Infrasound
Infrasound is sound with frequencies below 20 Hz. It is produced by natural events such as earthquakes, volcanic eruptions and ocean waves.
- Humans cannot hear infrasound but may feel it as vibrations
- Elephants use infrasound to communicate over long distances
- Infrasound monitoring detects nuclear explosions and tracks volcanic activity
- Some animals behave strangely before earthquakes, possibly sensing infrasound
Ultrasound
Ultrasound is sound with frequencies above 20,000 Hz. It has many practical applications because it is safe (non-ionising) and reflects well at boundaries between different media.
Medical Ultrasound (Pre-natal Scanning)
- Ultrasound waves are directed into the body using a transducer
- When the waves meet a boundary between different tissues, some are reflected back
- The transducer detects the returning echoes
- The timing and intensity of echoes are processed by a computer to build up an image
- Ultrasound is non-ionising, so it is safer than X-rays for imaging soft tissue and foetuses
Industrial Ultrasound
- Finding flaws in materials: ultrasound enters the material and reflects from cracks or boundaries
- Quality control in manufacturing (welds, pipes, metal castings)
- Cleaning delicate instruments using high-frequency vibrations in a cleaning solution
Echo Sounding and Sonar
Echo sounding uses ultrasound pulses to measure the depth of water or detect objects underwater. A pulse of ultrasound is sent downwards and the time taken for the echo to return is measured.
Depth Calculation
Distance = Speed × Time
The wave travels to the object AND back, so:
Depth = (Speed of sound in water × Time) / 2
Worked Example
A ship sends an ultrasound pulse to the sea floor. The echo returns after 0.8 s. The speed of sound in water is 1500 m/s. Calculate the depth of the sea.
Solution:
Total distance = speed × time = 1500 × 0.8 = 1200 m
Depth = 1200 / 2 = 600 m
Sonar (Sound Navigation and Ranging) is used by ships and submarines to detect objects underwater. Ultrasound pulses are emitted and the time delay for returning echoes is used to calculate distances. Dolphins and bats use a biological form of sonar called echolocation.
Comparison of Sound Wave Types
| Feature | Sound (Audible) | Ultrasound | Infrasound |
|---|---|---|---|
| Frequency range | 20 – 20,000 Hz | > 20,000 Hz | < 20 Hz |
| Human hearing | Can be heard | Cannot be heard | Cannot be heard |
| Medical uses | Stethoscopes | Pre-natal scanning, organ imaging | Limited |
| Industrial uses | Limited | Flaw detection, cleaning | Monitoring earthquakes |
| Animal examples | Most animals | Bats, dolphins | Elephants, whales |
Practice Questions
1. Explain why sound cannot travel through a vacuum. [2 marks]
Sound is a longitudinal wave that requires a medium to travel through. In a vacuum there are no particles to vibrate and pass on the compressions and rarefactions, so sound cannot propagate.
2. A ship uses echo sounding. The ultrasound pulse returns after 1.2 s. The speed of sound in water is 1500 m/s. Calculate the depth of the sea. [3 marks]
Total distance = 1500 × 1.2 = 1800 m. Depth = 1800 / 2 = 900 m.
3. Explain why ultrasound is used instead of X-rays for pre-natal scanning. [2 marks]
Ultrasound is non-ionising so it does not damage DNA or cells, making it safe for a developing foetus. X-rays are ionising and could harm the baby.
4. State the human hearing range and describe how it changes with age. [2 marks]
The human hearing range is approximately 20 Hz to 20,000 Hz. As people age, the upper limit decreases, meaning older people cannot hear as high frequencies.
5. Explain how ultrasound can be used to detect a crack inside a metal pipe. [3 marks]
An ultrasound pulse is sent into the metal. When it meets a crack (a boundary between metal and air), some ultrasound is reflected back early. The transducer detects this reflected pulse and the timing indicates the position of the crack within the pipe.
Maths Skills
Calculating Distance from Echo Times
Distance from Echo
distance = speed × time
depth = (speed of sound × time for echo) / 2
Remember: the wave travels to the object AND back, so you must halve the total distance (or total time) to find the one-way distance.
Worked Example 1: Echo Distance
A person stands 50 m from a cliff and claps their hands. The echo returns after 0.29 s. Calculate the speed of sound.
Total distance = 2 × 50 = 100 m
Speed = distance / time = 100 / 0.29 = 345 m/s
Worked Example 2: Ultrasound Depth
An ultrasound pulse is sent into the body. The echo from a boundary returns after 4.0 × 10⁻⁵ s. The speed of ultrasound in tissue is 1540 m/s. Calculate the depth of the boundary.
Total distance = 1540 × 4.0 × 10⁻⁵ = 6.16 × 10⁻² m
Depth = 6.16 × 10⁻² / 2 = 3.08 × 10⁻² m = 3.08 cm
Frequency Ranges
- Audible sound: 20 Hz to 20,000 Hz (2 × 10⁰ Hz)
- Ultrasound: above 20,000 Hz (2 × 10⁰ Hz)
- Infrasound: below 20 Hz
- When solving problems, always check whether you need to convert units (e.g. kHz to Hz: 1 kHz = 1000 Hz)
Frequency Conversion
Medical ultrasound typically uses 3.5 MHz. Convert to Hz: 3.5 MHz = 3.5 × 10⁶ Hz = 3,500,000 Hz. This is well above the human hearing range.
Common Misconceptions
"Sound travels fastest in air because air has less resistance." Sound travels fastest in solids and slowest in gases. In solids, particles are closer together and more tightly bonded, so vibrations pass from particle to particle more quickly. Steel: ~5000 m/s, water: ~1500 m/s, air: ~340 m/s.
"Ultrasound is a type of radiation and is therefore dangerous like X-rays." Ultrasound is a high-frequency sound wave. It is a longitudinal mechanical wave, not electromagnetic radiation. It is non-ionising, meaning it does not have enough energy to damage DNA or cells. This is why ultrasound is considered safe for pre-natal scanning, unlike X-rays which are ionising and can harm a developing foetus.
"A louder sound travels faster than a quieter sound." The speed of sound depends only on the medium (and its temperature), not on the amplitude (loudness). A very loud sound and a very quiet sound travel at the same speed through the same medium. Amplitude affects the energy carried, not the speed.
6-Mark Extended Question
Explain how ultrasound is used in medical imaging and discuss its advantages over X-ray imaging. [6 marks]
Ultrasound imaging works by sending high-frequency sound waves (above 20,000 Hz) into the body using a transducer. When the ultrasound meets a boundary between different tissues (e.g. between fluid and bone, or between muscle and fat), some of the wave is reflected back as an echo while some continues. The transducer detects the returning echoes and a computer processes the timing and intensity of the echoes to build up an image. The time taken for each echo to return tells us the depth of the boundary, because depth = (speed of sound in tissue × time) / 2. The intensity of the echo tells us about the nature of the boundary. Ultrasound has several advantages over X-ray imaging: it is non-ionising, so it does not damage DNA or cells, making it safe for imaging foetuses and soft tissue; it can distinguish between different soft tissues that X-rays cannot; it produces real-time moving images; and it is painless and non-invasive. X-rays are ionising and can cause cancer with repeated exposure, so they are not used for routine pre-natal scanning. However, X-rays are better for imaging bone because bone absorbs X-rays strongly, producing clear contrast with soft tissue.
AO3: Analyse and Evaluate
An ultrasound probe is used to scan internal tissue. The speed of ultrasound in soft tissue is 1540 m/s. The probe receives the following echoes:
- Echo 1 returns after 13.0 μs
- Echo 2 returns after 26.0 μs
- Echo 3 returns after 52.0 μs
(a) Calculate the depth of each boundary.
(b) Identify which boundary separation is the largest and calculate the distance between boundaries 1 and 2.
(c) Echo 3 has a much weaker signal than Echo 1. Explain what this tells you about the boundary that produced Echo 3.
(a) Depth = (speed × time) / 2
Boundary 1: depth = (1540 × 13.0 × 10⁻⁶) / 2 = (1540 × 1.3 × 10⁻⁵) / 2 = 0.02002 / 2 = 0.01001 m ≈ 1.0 cm
Boundary 2: depth = (1540 × 26.0 × 10⁻⁶) / 2 = 0.04004 / 2 = 0.02002 m ≈ 2.0 cm
Boundary 3: depth = (1540 × 52.0 × 10⁻⁶) / 2 = 0.08008 / 2 = 0.04004 m ≈ 4.0 cm
(b) Distance between boundaries 1 and 2 = 2.0 – 1.0 = 1.0 cm. Distance between boundaries 2 and 3 = 4.0 – 2.0 = 2.0 cm. The largest separation is between boundaries 2 and 3 (2.0 cm).
(c) The weaker signal from Echo 3 suggests that the boundary at 4.0 cm depth has a smaller difference in acoustic impedance (density/stiffness) between the two tissues. A smaller difference means less ultrasound is reflected and more is transmitted through, so the echo is weaker. It could also be partly due to absorption of ultrasound energy by the tissue above, reducing the signal that reaches deeper boundaries.
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