Sound production and propagation

Sound begins when a source vibrates, moving back and forth. The vibrating source causes particles in the surrounding material to vibrate. These particles affect neighbouring particles, passing the disturbance through the material. The material through which sound travels is called the medium.

Sound needs a material medium because the disturbance is passed from particle to particle. It cannot travel through a vacuum, where there are no particles to pass on the vibrations.

Sound as a longitudinal wave

A sound wave is longitudinal: particles of the medium vibrate back and forth parallel to the direction in which the wave travels. As they vibrate, they produce alternating regions of:

• Compression, where particles are closer together.
• Rarefaction, where particles are farther apart.

The compressions and rarefactions travel through the medium as particles pass the disturbance to their neighbours. The particles themselves vibrate about their positions; they do not travel along with the wave as a whole. In this way, sound transfers energy through the medium without carrying the medium as a whole with it.

Sound amplitude and loudness

A sound wave carries vibrations through a material such as air. The amplitude of the wave measures the size of those vibrations: it is the greatest distance the vibrating particles move from their resting positions.

A sound wave with a greater amplitude is heard as louder. A wave with a smaller amplitude is heard as quieter.

Loudness is associated with amplitude, not frequency. Frequency determines a sound’s pitch: how high or low it sounds. A sound can have the same pitch whether it is loud or quiet; changing its amplitude changes its loudness without changing its pitch.

Sound frequency and pitch

A sound is produced by vibrations. The frequency of a sound wave is the number of vibrations each second. It is measured in hertz, with the symbol $$\text{Hz}$$. For example, a frequency of $$200\ \text{Hz}$$ means there are 200 vibrations each second.

Pitch describes how high or low a sound seems. A higher frequency produces a higher-pitched sound; a lower frequency produces a lower-pitched sound. For example, a sound at $$400\ \text{Hz}$$ has a higher pitch than a sound at $$200\ \text{Hz}$$.

Pitch is distinct from loudness, which describes how loud or quiet a sound seems. A high-pitched sound is not necessarily loud, and a low-pitched sound is not necessarily quiet.

Human hearing range and ultrasound

The frequency of a sound is the number of vibrations each second. It is measured in hertz ($$\text{Hz}$$). A higher frequency corresponds to a higher-pitched sound.

Humans can typically hear sounds with frequencies from approximately $$20\ \text{Hz}$$ to $$20{,}000\ \text{Hz}$$. This is an approximate range: the limits vary between people.

Ultrasound is sound with a frequency higher than $$20{,}000\ \text{Hz}$$. Since $$20{,}000\ \text{Hz} = 20\ \text{kHz}$$, ultrasound is also described as sound above $$20\ \text{kHz}$$. It lies above the upper limit of the approximate human hearing range, so humans cannot normally hear it.

Measuring the speed of sound in air

Sound takes time to travel through air. Its speed can be estimated by measuring the distance it travels and the time it takes to travel that distance. The speed of sound in air is approximately $$330–350\ \mathrm{m/s}$$.

Measuring the distance and time

Place an observer a measured distance from a source that produces a sound and a visible signal at the same time. The observer starts a timer when they see the signal and stops it when they hear the sound.

Light travels much faster than sound, so its travel time is negligible compared with the sound travel time. The measured interval is therefore approximately the time taken for sound to travel from the source to the observer.

Calculating the speed of sound

Divide the measured distance by the measured time:

Here, $$v$$ is the estimated speed in metres per second, $$d$$ is the distance in metres, and $$t$$ is the time in seconds.

Repeat the measurement and average the results to improve the estimate. Repeats help reduce the effect of variation in the measured times, including variation caused by the observer's reaction time.

Echoes

An echo is a sound heard after sound waves reflect from a surface. For example, sound waves can travel towards a wall, reflect from it and return to a listener.

The sound travelling directly from the source reaches the listener first. The reflected sound travels by a longer route, so it arrives later. If the delay is long enough, the listener hears the reflected sound separately as an echo.

Speed of sound in different media

Sound travels through a material, or medium, as a disturbance passed from one part of the material to the next. How quickly this disturbance travels depends on the physical properties of the medium.

In general, sound travels fastest in solids, slower in liquids and slowest in gases. This is a general pattern, not a rule that applies to every combination of materials.

The speed depends on both how strongly the medium resists deformation and its density. A medium that resists deformation more strongly tends to pass the disturbance along faster. Greater density, on its own, tends to make the disturbance travel more slowly because more material must be set in motion. The actual speed depends on these properties together.

Ultrasound testing of materials

Ultrasound can reveal internal flaws in a material without damaging it. This is called non-destructive testing.

A short pulse of ultrasound is sent into the material. When the pulse reaches a boundary, some of it is reflected back. A crack or another internal flaw can create such a boundary, producing a reflected pulse that a detector can pick up. The far surface of the material can also reflect a pulse, so an echo returning before the far-surface echo may reveal an internal flaw.

Finding the position of a flaw

The time between sending a pulse and receiving its echo shows how far the pulse travelled. The pulse travels from the surface to the flaw and back again, so the distance to the flaw is half the total distance travelled:

Here, $$d$$ is the distance from the point where the pulse enters the material to the flaw, $$v$$ is the speed of ultrasound in the material, and $$t$$ is the time taken for the echo to return. If the pulse travels straight into the material, $$d$$ is the depth of the flaw.

Ultrasound medical scanning

Ultrasound scanning uses pulses of high-frequency sound to produce images of soft tissue inside the body. A device called a transducer sends the pulses into the body and detects the echoes that return.

As a pulse travels through the body, some of the sound is reflected at a boundary between different tissues. The reflected sound travels back to the transducer as an echo. Sound that continues beyond the boundary can produce further echoes at deeper boundaries.

Ultrasound scanning: Finding the depth of a boundary

A deeper boundary produces an echo that takes longer to return. If the speed of sound in the tissue is known, the depth can be calculated from the time taken for the echo to return:

Here, $$d$$ is the depth, $$v$$ is the speed of sound in the tissue and $$t$$ is the time between sending the pulse and receiving its echo. The distance is divided by two because the sound travels to the boundary and back.

The scanner uses the detected echoes and their return times to construct an image showing the positions of tissue boundaries.

Sonar

Sonar uses pulses of ultrasound and their echoes to find the distance to an object underwater or the depth of water. Ultrasound is sound with a frequency above the range of human hearing.

A sonar device sends a pulse through the water. The pulse reflects from an object or the seabed and returns to a detector as an echo. The device measures the time between sending the pulse and receiving the echo.

Calculating distance using sonar

The measured echo time covers both the outward and return journeys. Multiplying the speed of sound in water by this time gives the total distance travelled by the pulse, so the one-way distance is half of that:

Here, $$d$$ is the one-way distance to the object or seabed, $$v$$ is the speed of sound in water, and $$t$$ is the echo time. If $$v$$ is in metres per second and $$t$$ is in seconds, $$d$$ is in metres.

For example, if the speed of sound in water is $$1500\ \text{m/s}$$ and an echo returns after $$0.40\ \text{s}$$, the pulse has travelled $$600\ \text{m}$$ in total. The distance to the object or seabed is therefore $$300\ \text{m}$$.