Sound Waves

What is a Sound Wave?

A sound wave is produced when an object vibrates. A loudspeaker cone moving back and forth, a guitar string twanging, or your vocal cords all push on the surrounding air particles and set them oscillating.

Sound is a longitudinal wave. This means the particles of the medium vibrate parallel to (back and forth along) the direction the wave travels, not at right angles to it like a water wave. As the source moves forward it squashes particles together; as it moves back it spreads them out. These squashes and stretches travel outwards as the sound.

Key terms Longitudinal wave — a wave in which the particle vibrations are parallel to the direction of energy transfer.

Compression — a region where particles are pushed close together (higher pressure).

Rarefaction — a region where particles are spread apart (lower pressure).

Crucially, a sound wave needs a medium (a material such as a gas, liquid or solid) to travel through, because it relies on particles passing the vibration along from one to the next. With no particles, there is nothing to vibrate.

Watch out Sound cannot travel through a vacuum. In space, no matter how big the explosion, you would hear nothing. A famous demonstration is an electric bell ringing inside a glass jar: as a pump removes the air, the sound fades to silence even though you can still see the hammer striking.

Compressions and Rarefactions

We picture a sound wave as a pattern of compressions and rarefactions moving away from the source. Where particles bunch up, the air pressure is slightly higher; where they spread out, the pressure is slightly lower.

Notice that each particle only vibrates about a fixed point — it does not travel along with the wave. It is the pattern of compressions and rarefactions, and the energy, that move forward.

The Speed of Sound

Sound travels through air at roughly 340 m/s (about 1 200 km/h). That is fast, but far slower than light. This is why you see a flash of lightning almost instantly but hear the thunder seconds later, and why a distant batsman's swing is seen before the crack is heard.

The speed depends on the medium. Sound travels faster in liquids than in gases, and fastest in solids, because the particles are closer together and pass the vibration on more quickly.

Exam tip When asked why sound is faster in solids, say the particles are closer together, so vibrations are passed on more quickly from particle to particle. Do not write "more dense" on its own — link it to particle spacing.

Frequency and Pitch, Amplitude and Loudness

Two properties of a sound wave map onto what we hear:

Frequency (measured in hertz, Hz) is the number of complete waves per second. A higher frequency gives a higher pitch (a squeakier, higher note). A low frequency gives a low, booming note.
Amplitude is the maximum disturbance of the wave (how big the compressions are). A larger amplitude gives a louder sound. A small amplitude is quiet.

Key terms Pitch — how high or low a note sounds; set by the frequency.

Loudness — how loud a sound is; set by the amplitude.

The Audible Range

The human ear can only detect a limited range of frequencies, called the audible range:

$$20 \text{ Hz} \;\text{to}\; 20\,000 \text{ Hz}$$

Sounds below 20 Hz (infrasound) and above 20 000 Hz (ultrasound) cannot be heard by humans. The upper limit drops as we get older. Many animals hear further: dogs respond to frequencies well above 20 kHz, which is how a "silent" dog whistle works.

Displaying Sound on an Oscilloscope

A microphone turns a sound wave into an electrical signal. Feeding this into a cathode-ray oscilloscope (CRO) draws the wave on a screen, letting us compare sounds.

A higher-pitched sound has waves packed closer together (more waves per division — higher frequency).
A louder sound has taller waves (larger amplitude).

Exam tip To read a trace: count the waves across the screen to judge frequency/pitch, and measure the height to judge amplitude/loudness. "More waves = higher pitch; taller waves = louder."

Echoes and Measuring Distance

When sound hits a hard surface it is reflected. A reflected sound you hear after a short delay is an echo.

We can use echoes to measure distance or to find the speed of sound. The sound must travel to the surface and back, so it covers twice the distance $d$. If the round trip takes time $t$:

$$\text{speed} = \frac{2d}{t}$$

Worked example A student stands 170 m from a large cliff and claps once. She hears the echo 1.0 s later. Find the speed of sound in air.

The sound travels to the cliff and back, a total distance of $2 \times 170 = 340$ m, in $1.0$ s.

$$\text{speed} = \frac{2d}{t} = \frac{2 \times 170}{1.0} = \frac{340}{1.0} = 340 \text{ m/s}$$

Watch out Always remember the factor of 2. The single most common echo mistake is using $d$ instead of $2d$, which halves your answer.

Ultrasound and its Uses

Ultrasound is sound with a frequency above 20 000 Hz — too high for humans to hear. Because it can be sent in narrow beams and reflects off boundaries between different materials, it is extremely useful:

Medical scanning. Ultrasound pulses sent into the body reflect off boundaries between tissues. The reflections are processed into an image — most famously to check on a baby in the womb. Unlike X-rays, ultrasound does not use ionising radiation, so it is considered safe for this.
Sonar / measuring depth. A ship sends a pulse of ultrasound towards the seabed and times the echo. Using $\text{depth} = \dfrac{\text{speed} \times t}{2}$, it works out how deep the water is. The same idea detects shoals of fish or underwater objects.
Cleaning. Delicate items such as jewellery, lenses and electronic parts are placed in a liquid through which high-frequency ultrasound is passed. The vibrations shake dirt loose from awkward gaps without scratching.

Real world A trawler sends an ultrasound pulse to the seabed and the echo returns after 0.4 s. Sound travels at 1 500 m/s in seawater. The depth is $\frac{1500 \times 0.4}{2} = 300$ m — again, divide by 2 because the pulse makes a round trip.

Key terms Echo — a sound heard again after reflecting off a surface.

Ultrasound — sound of frequency above 20 000 Hz (above the human audible range).

Sonar — using reflected ultrasound pulses to measure distance or depth underwater.