Sound Waves and Ultrasound

(Separate Physics only) (Higher Tier only) Everything in this lesson is assessed only in AQA GCSE Physics at Higher Tier. It is not in Combined Science and not on Foundation papers.

Sound is a longitudinal wave made of vibrating particles, so it can travel through solids, liquids and gases. In a solid the particles are packed close together, so the vibrations pass on quickly and sound often travels faster than in air.

When sound reaches your ear, it works as a chain of vibrations:

1. The sound wave travels down the ear canal and reaches the ear drum.
2. The changing pressure of the wave makes the ear drum vibrate back and forth.
3. The ear drum passes these vibrations on to small bones and other structures inside the ear.
4. These are converted into signals sent to the brain, which we perceive as sound.

The specification asks you to describe how sound waves are converted to vibrations in solids and back again. The key point is that sound is a vibration, and any solid part it reaches (an ear drum, a microphone diaphragm, a wall) can be made to vibrate at the same frequency, carrying the sound onward.

Sound travels through a solid as vibrations of the particles. The ear drum is a solid membrane that vibrates when sound hits it, which is how the ear turns a sound wave into movement it can process.

The conversion of sound into vibrations of the ear drum and the other parts of the ear only works well over a limited range of frequencies. Outside this range the ear's structures cannot vibrate efficiently in response to the wave, so we do not hear the sound.

The normal range of human hearing is 20 Hz to 20 kHz (20,000 Hz). You should recall these limits.

Frequencies below 20 Hz (infrasound) and above 20 kHz (ultrasound) exist and carry energy, but the human ear cannot convert them into signals the brain registers. The upper limit tends to fall with age, but the standard figure examiners expect is 20 kHz. This limit is a direct consequence of the physical properties of the ear drum and the other vibrating parts: they respond over a restricted band of frequencies.

Ultrasound is sound with a frequency above 20 kHz, the upper limit of human hearing. Its usefulness comes from one key behaviour: when ultrasound meets a boundary between two different media, part of it is reflected and part carries on. This is partial reflection.

By sending a pulse of ultrasound into an object and timing how long each reflection takes to return, the distance to each boundary can be calculated. The wave travels to the boundary and back, so the total path is twice the depth:

$\text{distance to boundary}=\frac{\text{speed}\times \text{time}}{2}$

This is the distance–time relationship $s=vt$ (recall and apply), with the factor of two because the pulse makes a round trip.

Worked example — ultrasound scan. An ultrasound pulse travels at 1500 m/s through body tissue and its reflection returns after 0.00004 s (40 microseconds). Find the depth of the boundary.

$\text{depth}=\frac{1500\times 0.00004}{2}=\frac{0.06}{2}=0.03\text{ m}$

The boundary is 0.03 m (3 cm) below the surface. Repeating this across the body builds up a medical image, such as a scan of an unborn baby, without any ionising radiation. The same idea is used in industry to find cracks and flaws inside metal parts.

Echo sounding uses high-frequency sound (often ultrasound) to detect objects and measure the depth of water. A pulse is sent downwards from a ship; it reflects off the seabed or a shoal of fish and returns. Timing the round trip gives the depth, using the same halving rule.

Worked example — measuring sea depth. A ship sends a sound pulse straight down and receives its echo after 0.08 s. Sound travels at 1500 m/s in seawater. Find the depth.

$\text{depth}=\frac{1500\times 0.08}{2}=\frac{120}{2}=60\text{ m}$

The seabed is 60 m below the ship. Echo sounding is used for mapping the sea floor, measuring water depth for navigation, and locating shoals of fish.

Seismic waves are produced by earthquakes and travel through the Earth. There are two types, and the difference between them reveals what the Earth is made of inside.

Seismic wave	Type	Travels through	Speed
P-wave (primary)	Longitudinal	Solids and liquids	Faster; arrives first
S-wave (secondary)	Transverse	Solids only	Slower; arrives later

Because a transverse wave needs the material to be rigid, S-waves cannot pass through a liquid. When earthquakes are detected around the world, seismometers show a large region on the far side of the Earth that receives no S-waves at all (an S-wave shadow zone). The only explanation is that the S-waves have hit a liquid layer they cannot cross: the liquid outer core.

P-waves, being longitudinal, do travel through the core, but they change direction (refract) as they cross boundaries where the wave speed changes, and this bending shows there are separate layers with different properties. Together, the patterns of P-waves and S-waves give evidence for the size and structure of the Earth's core, including that the outer core is liquid.

P-waves are longitudinal and pass through solids and liquids. S-waves are transverse and only pass through solids. The S-wave shadow zone is the evidence that the outer core is liquid.

1. Forgetting to halve the time or distance

For ultrasound scans and echo sounding, the pulse travels to the boundary and back. The measured time covers the round trip, so divide the total distance by two to get the depth. Missing the halving doubles the answer.

2. Getting P-waves and S-waves the wrong way round

P-waves are longitudinal (Primary, and they Push, arriving first); S-waves are transverse (Secondary, Shear, and Stopped by liquids). Swapping them, or saying P-waves cannot cross liquids, reverses the whole argument about the core.

3. Confusing ultrasound frequency with the audible range

Ultrasound is defined as frequencies above 20 kHz. The audible range is 20 Hz to 20 kHz. Do not describe an audible sound as ultrasound.

4. Saying S-waves are stopped because they are too weak

S-waves cannot travel through liquids because they are transverse and liquids cannot support the sideways shearing motion. It is a property of the wave type, not a matter of the wave losing energy.

5. Writing the wrong hearing limits

The standard range is 20 Hz to 20 kHz. Note that 20 kHz means 20,000 Hz. Writing "20 Hz to 20 Hz" or "2 kHz" instead of 20 kHz is a common slip.