This note covers how sound is made and travels, what pitch and loudness depend on, how fast sound moves in different materials, how echoes are used to find distances, and what ultrasound is and how it is used. Sound links to everyday life, from music and hearing to medical scans and sonar.
Key ideas
How sound is produced and travels. Sound is made by a vibrating object, such as a guitar string, a loudspeaker cone or vocal cords. The vibrations pass to the particles of the surrounding material, and the sound travels as a longitudinal wave of compressions (high pressure) and rarefactions (low pressure).
Sound needs a medium (solid, liquid or gas) because it is passed from particle to particle. It cannot travel through a vacuum. This can be shown by pumping air out of a jar containing a ringing bell: the sound fades away although the bell is still seen vibrating.
Speed of sound. The speed depends on the material.
- Gases: slowest. In air it is about 330 to 340 m/s at room temperature.
- Liquids: faster. In water it is about 1500 m/s.
- Solids: fastest. In steel it is about 5000 m/s.
The particles in a solid are closer together and bonded more strongly, so each vibration is passed on more quickly. Sound travels hundreds of thousands of times slower than light, which is why you see lightning before you hear the thunder.
To measure the speed of sound in air, time how long a loud sound takes to travel a known distance. For example, stand 100 m or more from a large wall, make a short sharp sound and time the echo. Repeating the measurement and averaging reduces the effect of reaction time. Then use speed = distance ÷ time, and remember that for an echo the distance travelled is twice the distance to the wall.
Pitch and loudness.
- Pitch depends on frequency. A higher frequency gives a higher pitch.
- Loudness depends on amplitude. A larger amplitude gives a louder sound.
On an oscilloscope trace from a microphone, more waves across the screen means a higher frequency, and taller waves mean a larger amplitude.
Humans with normal hearing can detect frequencies from about 20 Hz to 20 000 Hz (20 kHz). The upper limit usually decreases with age.
Echoes. An echo is sound that has reflected from a hard surface. Hard, smooth surfaces reflect sound well. Soft, rough surfaces absorb it. If the distance to the surface is d and the sound takes a time t to go out and return, then:
2d = v × t, so d = v × t ÷ 2
Ultrasound. Ultrasound is sound with a frequency above 20 000 Hz, higher than humans can hear. It travels as a longitudinal wave in the same way as ordinary sound. Some of it is reflected at the boundary between two different materials, which gives echoes that can be timed.
- Medical imaging: in a pregnancy scan, pulses of ultrasound are sent into the body and partly reflected at the boundaries between different tissues. A computer uses the time of each echo to build up a picture. It is safer than X-rays, which can damage cells.
- Cleaning: ultrasound makes dirt and grease fall off delicate items such as jewellery in a bath of liquid.
- Flaw detection: ultrasound passes through metal. An echo from a hidden crack arrives earlier than the echo from the far side of the metal.
- Sonar: boats send out pulses of sound and time the echoes to measure the depth of water or to locate fish and wrecks.
Definitions and formulae
| Term or formula | Meaning / when to use |
|---|---|
| Compression / rarefaction | Region of a longitudinal wave where particles are squashed together / spread apart. |
| Pitch | How high or low a note sounds. Depends on frequency. |
| Loudness | How strong a sound seems. Depends on amplitude. |
| Audible range | About 20 Hz to 20 000 Hz for normal human hearing. |
| Ultrasound | Sound of frequency greater than 20 000 Hz. |
| v = distance ÷ time | Speed of sound from a measured distance and time. |
| v = f λ | Wave equation, used for sound waves as for any wave. |
| d = v t ÷ 2 | Distance to a reflecting surface from the time for the echo to return. |
Worked examples
Example 1 A flash of lightning is seen. The thunder is heard 3.0 s later. The speed of sound in air is 330 m/s. How far away is the lightning?
The light arrives almost instantly, so the time is the travel time of the sound.
distance = speed × time = 330 × 3.0 = 990 m.
Answer: 990 m (about 1.0 km)
Example 2 A research boat sends a pulse of sound down to the sea floor and detects the echo 0.80 s later. The speed of sound in sea water is 1500 m/s. Find the depth of the water.
The pulse travels down and back, so the total distance is 2d.
2d = 1500 × 0.80 = 1200 m.
d = 1200 ÷ 2 = 600 m.
Answer: 600 m
Example 3 A medical scanner sends a pulse of ultrasound into the body. The speed of ultrasound in soft tissue is 1540 m/s. An echo from an organ boundary returns after 52 μs (52 × 10−6 s). How deep is the boundary?
Total distance travelled = v × t = 1540 × 52 × 10−6 = 0.0801 m.
This is there and back, so depth = 0.0801 ÷ 2 = 0.0400 m.
Answer: 0.0400 m (4.00 cm)
Common errors
- Common error: forgetting to halve the distance in echo calculations. The sound travels to the surface and back.
- Common error: saying sound can travel through a vacuum, or drawing sound as a transverse wave. Sound is longitudinal and needs a medium.
- Common error: mixing up pitch and loudness. Frequency changes the pitch, and amplitude changes the loudness.
- Common error: saying that sound travels fastest in gases. It is fastest in solids and slowest in gases.
- Common error: forgetting to convert microseconds or kilohertz into seconds or hertz before calculating.
Exam tip: In an echo question, write "distance = speed × time" first, then say "this is the distance there and back" and divide by two so the step is not missed.
Check yourself
- A sound has a frequency of 440 Hz in air, where the speed of sound is 330 m/s. Find its wavelength.
Answer
λ = v ÷ f = 330 ÷ 440 = 0.750 m. - A person shouts towards a cliff and hears the echo 1.6 s later. The speed of sound is 330 m/s. How far away is the cliff?
Answer
Total distance = 330 × 1.6 = 528 m. Distance to cliff = 528 ÷ 2 = 264 m. - On an oscilloscope, a note is replaced by one with the same height of trace but twice as many waves across the screen. What has changed about the sound?
Answer
The frequency has doubled, so the pitch is higher. The amplitude (height) is the same, so the loudness is unchanged. - Why is ultrasound used instead of X-rays to scan an unborn baby?
Answer
Ultrasound is not ionising and does not damage living cells, whereas X-rays can damage cells and may cause cancer.