Sound and seismic waves

1. What a sound wave is

Where sound comes from. Sound is made when an object vibrates: a loudspeaker cone, a guitar string, your vocal cords. As the object moves forward, it pushes the air particles next to it closer together. As it moves back, it leaves a gap where they are more spread out. Each layer of air pushes on the next, so the pattern travels outwards.

Compression: a region where the particles are pushed closer together.

Rarefaction: a region where the particles are more spread out.

Sound is a longitudinal wave. The particles vibrate backwards and forwards along the direction the wave travels.

The air stays where it is. Each particle vibrates about the same spot and passes the energy on to the next. The wave travels; the air doesn’t.

Sound needs a medium: a solid, a liquid or a gas. It can’t travel through a vacuum, such as outer space, because there are no particles to pass the vibrations on.

2. Pitch, loudness and seeing a sound

Frequency: the number of vibrations each second, measured in hertz (Hz). A source vibrating at 500 Hz makes 500 waves every second. 1 kHz = 1000 Hz.

Pitch depends on frequency. The higher the frequency, the higher the pitch. A violin string vibrates faster than a cello string, so it plays higher notes.

Loudness depends on amplitude. The bigger the amplitude of the vibration, the louder the sound. A bigger amplitude means the wave carries more energy. Hit a drum harder and it vibrates with a bigger amplitude.

Seeing a sound on an oscilloscope. A microphone turns the sound into an electrical signal, and an oscilloscope draws that signal as a line across its screen. The line shows how the signal changes with time.

• A taller trace means a bigger amplitude: a louder sound.
• More waves across the screen means a higher frequency: a higher pitch.
• The trace looks like a transverse wave. The sound itself is still longitudinal.

Finding the frequency from the screen. Read off the time for one complete wave, the time period, T, using the screen’s time scale. Then:

frequency = 1 ÷ time period   (f = 1/T, with T in seconds)

Example: one complete wave covers 4 squares, and each square is 0.5 ms. T = 4 × 0.5 = 2 ms = 0.002 s, so f = 1 ÷ 0.002 = 500 Hz.

A pure note and a noise. A tuning fork, or a signal generator connected to a loudspeaker, makes a smooth wave that repeats regularly. A spoken word or a crash makes a jagged trace with no repeating pattern.

3. Sound passing from one material to another

Sound travels through solids and liquids as well as gases. When a sound wave reaches a solid, it makes the particles of the solid vibrate, and the wave carries on through it. That’s why you can hear someone talking through a closed door. On the far side, the vibrating door makes the air vibrate again.

The speed depends on the material. Sound is usually fastest in solids and slowest in gases.

What changes and what doesn’t. When sound passes from one material into another:

• the frequency stays the same. It is set by the source: every vibration that reaches the boundary makes one vibration on the other side.
• the speed changes.
• so the wavelength changes. From wave speed = frequency × wavelength (v = f λ), the wavelength is the speed divided by the frequency. Faster means a longer wavelength; slower means a shorter one.

Example: a 500 Hz sound in air (340 m/s) has a wavelength of 340 ÷ 500 = 0.68 m. When it passes into water (1500 m/s), it is still 500 Hz, and its wavelength becomes 1500 ÷ 500 = 3.0 m.

4. How you hear: inside the ear

Your ear does what section 3 describes. It turns sound waves in the air into vibrations of solid parts, then into signals your brain can read.

1. The outer ear collects the sound and channels it down the ear canal.
2. The sound waves make the ear drum, a thin, tight membrane, vibrate at the same frequency as the sound.
3. Three tiny bones in the middle ear pass the vibrations from the ear drum to the inner ear.
4. The vibrations pass into the liquid inside the cochlea, a coiled tube in the inner ear. They move tiny hair cells that line it.
5. The hair cells send electrical signals along the auditory nerve to the brain, which hears them as sound.

The key idea for exams: a sound wave in the air is converted into vibrations of solids (the ear drum and the bones), and then into electrical signals.

5. The limits of human hearing

Normal human hearing runs from 20 Hz to 20 kHz (20 000 Hz). Sounds outside this range are still sound waves; your ears just can’t detect them.

• Ultrasound: sound with a frequency above 20 000 Hz.
• Infrasound: sound with a frequency below 20 Hz.

Why the range is limited. Hearing only works if the ear drum and the small bones vibrate in step with the sound. Any solid object vibrates well over only a certain range of frequencies, set by its size, mass and stiffness. Outside that range, the ear drum and bones hardly vibrate at all, so almost nothing reaches the cochlea. However loud the sound is, you won’t hear it.

The range you hear best. The small bones pass on frequencies from about 1 kHz to 3 kHz most efficiently, so a quiet sound in this range is easier to hear than an equally quiet one outside it.

Hearing changes with age. The range gets narrower as people get older, and the highest frequencies go first. The hair cells in the cochlea that respond to high frequencies are gradually lost, and loud noise damages them too. That’s why an older adult may not hear a high-pitched sound that a teenager can.

Other animals hear different ranges. Dogs and bats can hear ultrasound. Elephants communicate using infrasound.

6. Ultrasound and echoes

Ultrasound has a frequency too high for humans to hear, but it behaves like any other sound. That makes it useful for looking inside things you can’t see into.

Partial reflection. When ultrasound meets a boundary between two different materials, for example two types of body tissue, part of it is reflected and the rest carries on to the next boundary. So one pulse sent in comes back as a series of echoes, one from each boundary.

Timing the echoes. A device called a transducer sends out short pulses of ultrasound and detects the echoes. The further away a boundary is, the longer its echo takes to come back.

Working out the distance. The echo travels to the boundary and back, so:

distance travelled = speed × time
distance to the boundary = ½ × speed × time

Example: ultrasound travels through soft tissue at about 1500 m/s. An echo comes back after 0.000 08 s (80 µs). Distance travelled = 1500 × 0.000 08 = 0.12 m. The boundary is half of that: 0.06 m, or 6 cm, below the skin.

7. Ultrasound imaging in medicine and industry

Scanning the body. The transducer is moved across the skin. The echoes from each tissue boundary are timed, and a computer uses them to build up a picture of what’s inside.

• Prenatal scans of a baby in the womb.
• Images of organs such as the kidneys, and of damaged ligaments and muscles.

Why ultrasound, and not X-rays, for a baby scan:

• Ultrasound is non-ionising. It doesn’t have enough energy to ionise atoms, so it doesn’t damage cells the way X-rays can. That makes it safe for the mother and the unborn baby.
• Ultrasound reflects from the boundaries between soft tissues, so it can show organs. X-rays pass through soft tissue and mostly show bone.

Finding flaws in metal. A crack inside a metal casting or weld is a boundary too. A pulse sent into the metal reflects partly from the crack and partly from the far side. On the screen there’s an extra spike between the front and back spikes. Its position shows how deep the crack is. The part doesn’t need to be cut open to check it.

8. Echo sounding and sonar

Echo sounding uses pulses of high-frequency sound to measure the depth of water and to find objects under water.

1. A transmitter under the ship sends a pulse down.
2. The pulse reflects from the seabed.
3. A receiver on the ship detects the echo.
4. The time taken is measured, and the depth is ½ × speed × time.

Example: sound travels through sea water at about 1500 m/s. The echo comes back after 0.4 s. Depth = ½ × 1500 × 0.4 = 300 m.

The same method finds shoals of fish, shipwrecks and submarines: anything that reflects the pulse sends back an earlier echo. This use of echoes is called sonar (SOund Navigation And Ranging).

9. Infrasound and seismic waves: looking inside the Earth

AQA, Edexcel and OCR B. OCR A’s specification doesn’t include seismic waves.

Nobody has drilled anywhere near the Earth’s core. What we know about it comes from studying waves that have travelled through it.

Seismic waves are produced by earthquakes and travel through the Earth. Most have low frequencies, well below 20 Hz, so they are infrasound. Detectors called seismometers, at stations around the world, record when they arrive.

10. The mistakes that cost marks

1. “The frequency changes when sound goes into water.” It doesn’t. Write: “the frequency stays the same; the speed changes, so the wavelength changes.”
2. Forgetting to halve. An echo goes there and back. Distance to the boundary = ½ × speed × time.
3. “We can’t hear ultrasound because it’s too quiet.” Loudness has nothing to do with it. Write: “its frequency is above 20 000 Hz, the upper limit of human hearing.”
4. “The brain can’t process high frequencies.” For why hearing is limited, write: “the ear drum and small bones can only vibrate over a limited range of frequencies.”
5. “Ultrasound is safer because it’s weaker.” Write: “ultrasound is non-ionising, so it doesn’t damage cells the way X-rays can.”
6. “S-waves can’t travel through the core.” Be exact: “S-waves can’t travel through liquids, and the outer core is liquid.”
7. Calling sound transverse because of the oscilloscope trace. The screen draws it as a line; sound is longitudinal.
8. Unit slips. 20 kHz = 20 000 Hz. 1 ms = 0.001 s; 1 µs = 0.000 001 s. Change to hertz and seconds before putting numbers into an equation.

Quick checklist

• I can describe how a vibrating object makes a sound wave, using compression and rarefaction.
• I can explain why sound can’t travel through a vacuum.
• I can link pitch to frequency and loudness to amplitude, and read both from an oscilloscope trace.
• I can work out a frequency from a time period.
• I can say what happens to frequency, speed and wavelength when sound passes into a new material.
• I can describe what reflection, transmission and absorption mean at a boundary.
• I can describe how the ear turns sound waves into signals to the brain.
• I can give other examples of sound being converted to vibrations in solids.
• I can state the range of human hearing, and define ultrasound and infrasound.
• I can explain why hearing works only over a limited range, and why it changes with age.
• I can work out a depth or distance from an echo time.
• I can explain how ultrasound is used in medical scans and to find flaws in metal.
• I can explain why ultrasound is used instead of X-rays to scan an unborn baby.
• I can describe how echo sounding measures the depth of the sea.
• I can describe P-waves and S-waves, and explain what they tell us about the Earth’s core.