OxfordAQA International GCSE Physics: Wave properties, sound and ultrasound (9203)

This guide is written for the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards. It covers sections 3.3.1 (general properties of waves) and 3.3.3 (sound and ultrasound). The qualification is untiered. Parts 3.3.3 d to h are for the full Physics award only and are marked “P” in the specification.

Use the course hub to see the other topics and the printable checklist to tick off each outcome. When you want to test yourself, use the revision notes, the practice questions and the 10-minute diagnostics. The exam preparation page covers general technique.

What this unit covers

Section	What you must be able to do
3.3.1 a	Define a wave: an oscillating source transfers energy and information without transferring matter
3.3.1 b, c	Describe transverse and longitudinal waves, including compressions and rarefactions
3.3.1 d	Give examples of each type
3.3.1 e	Describe reflection, transmission and absorption at a boundary
3.3.1 f	Describe refraction and diffraction, and when diffraction is appreciable
3.3.1 g	Explain frequency, wavelength, period, amplitude and wavefront
3.3.1 h	Use wave speed = frequency x wavelength
3.3.3 a to c	Sound as a longitudinal wave, hearing range, pitch, loudness, echoes and diffraction
3.3.3 d to f (P)	Ultrasound, how it is produced, partial reflection at boundaries
3.3.3 g (P)	Calculate distances between interfaces using s = vt, including oscilloscope traces
3.3.3 h (P)	Medical uses: prenatal scanning and kidney stone removal

What a wave is (3.3.1 a)

A wave starts as a disturbance made by a vibrating source. As it travels it carries energy and information onwards along its path, but the material it passes through is not carried along. A cork floating on a lake rises and falls as ripples go by. The cork does not travel across the pond with the ripples, so the water is not carried along. Energy is.

Transverse and longitudinal waves (3.3.1 b to d)

In a transverse wave the oscillations are at right angles (perpendicular) to the direction in which energy moves. Shake the end of a long rope up and down while the pulse travels along the rope: the rope moves up and down, the energy moves along.

In a longitudinal wave the vibrations lie along the same line as the direction the energy travels. Push and pull the end of a stretched spring along its length. Coils bunch up in regions called compressions and spread out in regions called rarefactions. These move along the spring, while each coil only shifts to and fro.

Type	Oscillation compared with travel	Examples
Transverse	Perpendicular	Electromagnetic waves, water waves, waves on a rope
Longitudinal	Parallel	Sound waves

Mechanical waves may be either type. Sound needs a medium (its particles vibrate), so it cannot travel through a vacuum.

Describing a wave (3.3.1 g)

Be ready to explain each term in your own words.

• Amplitude: the maximum displacement of a point from its undisturbed (rest) position.
• Wavelength, λ: the span of one full wave, found by measuring from a point to the matching point on the next wave (crest to crest, or compression to compression), in metres.
• Frequency, f: how many complete waves go past a given point in one second. The unit is the hertz (Hz).
• Period, T: how long one complete wave takes to go past, in seconds. T = 1/f.
• Wavefront: a line joining points that are at the same stage of their oscillation, such as all the crests of a water wave. Wavefronts move in the direction of travel at right angles to themselves.

The wave equation (3.3.1 h)

The wave speed, frequency and wavelength are linked by:

wave speed (m/s) = frequency (Hz) x wavelength (m), or v = fλ

Think of the crests: f of them pass a fixed point every second, and the spacing between neighbours is λ, so the pattern moves on by fλ each second.

Worked example 1. A wave on a rope has a frequency of 2.5 Hz and a wavelength of 0.80 m. Find its speed and period.

v = fλ = 2.5 x 0.80 = 2.0 m/s
T = 1/f = 1/2.5 = 0.40 s

Worked example 2. A ripple tank wave travels at 0.18 m/s with a wavelength of 0.012 m. Find the frequency.

f = v/λ = 0.18 / 0.012 = 15 Hz

Reflection, transmission and absorption (3.3.1 e)

When a wave reaches a boundary between two different materials, it can be reflected (bounced back), transmitted (pass into the second material) or absorbed (its energy is transferred to the material, which warms slightly). Often it is a combination. Sound meeting a wall is partly reflected, partly absorbed by the wall and partly transmitted, which is why you can still hear a radio in the next room. Soft, rough materials such as curtains absorb more sound; hard, smooth ones reflect more.

Refraction and diffraction (3.3.1 f)

Refraction happens because a wave’s speed changes when it passes into a different material or depth. When a wave crosses a boundary at an angle, the change of speed also changes the direction. The source decides the frequency and the boundary cannot alter it, so a change of speed means a change of wavelength.

Worked example 3. In a ripple tank the frequency is 12 Hz. Waves in deep water have a wavelength of 0.020 m. In the shallow part the wavelength is 0.0125 m. Find the speed in each region.

Deep:    v = 12 x 0.020  = 0.24 m/s
Shallow: v = 12 x 0.0125 = 0.15 m/s

The waves slow down in the shallow water, so the wavelength shortens and the wavefronts bunch up.

Diffraction is the spreading of waves as they pass through a narrow gap or past the edge of an obstacle. Diffraction is appreciable only when the wavelength is comparable to the size of the gap or obstacle. A wide gap compared with the wavelength gives little spreading. A gap about one wavelength wide gives strong, nearly circular spreading.

This idea is applied in three places in the specification: reducing diffraction in optical instruments, ultrasound in medicine and radio wave reception. Light has a very short wavelength, so it diffracts very little through the aperture of an instrument. Ultrasound has a very short wavelength too, so it travels as a narrow beam. Long-wavelength radio waves diffract round hills and buildings, which helps reception where there is no direct line of sight.

Sound waves (3.3.3 a to c)

Sound is a longitudinal wave. A vibrating source, such as a loudspeaker cone, pushes and pulls on the air, making a series of compressions and rarefactions. The air particles vibrate back and forth, and the ear detects these vibrations as sound. People hear frequencies from roughly 20 Hz up to 20 000 Hz (20 kHz). The structure of the ear is not required.

• Pitch depends on the frequency of vibration of the source. Higher frequency, higher pitch.
• Loudness is related to the amplitude of the disturbance. Larger amplitude, louder sound.

An oscilloscope connected to a microphone shows the pressure variation as a wave trace. A louder note gives a taller trace. A higher note fits more cycles across the screen.

Worked example 4. The time base of an oscilloscope is set to 0.5 ms per division. One complete cycle of a note takes 4 divisions. Find the frequency.

T = 4 x 0.5 ms = 2.0 ms = 0.0020 s
f = 1/T = 1/0.0020 = 500 Hz

Worked example 5. Sound travels at 340 m/s in air. Find the wavelength of a 680 Hz note, and the wavelengths at the ends of the hearing range.

680 Hz:    λ = 340/680    = 0.50 m
20 Hz:     λ = 340/20     = 17 m
20 000 Hz: λ = 340/20 000 = 0.017 m

Sound is reflected (an echo is a reflected sound heard after the original) and diffracted. You hear someone talking round a corner because sound, with wavelengths of metres, diffracts well through doorways.

Ultrasound (3.3.3 d to f, P)

Ultrasound is sound whose frequency lies higher than anything a person can hear, so above 20 000 Hz. Electronic systems produce it: an alternating electrical signal is applied to a transducer, which vibrates at the same high frequency. The same transducer can also detect returning ultrasound and convert it to an electrical signal.

When ultrasound meets a boundary between two different media, it is partially reflected. Some of the pulse reflects back and some carries on. A detector measures the time for each reflection to arrive. That time gives the distance to the boundary.

Calculating distances (3.3.3 g, P)

The specification gives the distance between interfaces as s = vt, with v the speed of the wave and t the time it takes. A pulse that reflects has travelled to the boundary and back, so the time you read from a trace covers a double journey. For a distance to a boundary, use the time for the one-way trip, which is half the measured time.

Worked example 6. A clap is made 1.6 s before the echo from a cliff is heard. The speed of sound is 330 m/s. How far away is the cliff?

One-way time = 1.6 / 2 = 0.80 s
s = vt = 330 x 0.80 = 264 m, so about 260 m

Worked example 7. Ultrasound has a frequency of 3.5 MHz and travels at 1500 m/s in soft tissue. Find its wavelength.

λ = v/f = 1500 / 3 500 000 = 0.00043 m (0.43 mm)

Worked example 8. An oscilloscope shows a transmitted pulse at 0 and echoes from two boundaries at 3 divisions and 7 divisions. The time base is 20 µs per division, and the speed is 1500 m/s.

Echo 1: round trip 3 x 20 = 60 µs, one way 30 µs = 3.0 x 10^-5 s
        s = 1500 x 3.0 x 10^-5 = 0.045 m
Echo 2: round trip 140 µs, one way 70 µs
        s = 1500 x 7.0 x 10^-5 = 0.105 m
Distance between the boundaries = 0.105 - 0.045 = 0.060 m (6.0 cm)

Medical uses (3.3.3 h, P)

• Prenatal scanning: pulses are sent into the body, and reflections from the boundaries between tissues and fluid are timed and processed into an image of the fetus. Ultrasound is non-ionising, so it is used instead of X-rays here.
• Kidney stones: a focused beam of high-intensity ultrasound is aimed at the stone, which breaks into small pieces that can pass out of the body in urine, avoiding surgery.

Common errors

1. Using the whole echo time in s = vt for a distance to the boundary. Halve it first.
2. Saying the particles travel along with the wave. They oscillate about a fixed position.
3. Saying loudness depends on frequency. It depends on amplitude.
4. Saying that refraction changes frequency. It changes speed and wavelength.
5. Forgetting to convert units: µs to s, MHz to Hz, ms to s.
6. Describing diffraction without mentioning that the wavelength must be comparable to the gap.

Official syllabus

OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards, published by OxfordAQA. This page covers sections 3.3.1 and 3.3.3.