Sound Waves

Nature of Sound Waves

Sound waves are longitudinal waves. This means the vibrations of the particles in the medium are parallel to the direction the wave travels. When an object vibrates, it causes the particles in the surrounding medium (air, fluids, or solids) to vibrate too, creating regions of compression and rarefaction.

• Compression: Particles are pushed close together, increasing pressure.
• Rarefaction: Particles are spread further apart, decreasing pressure.

These alternating compressions and rarefactions travel through the medium as the sound wave moves.

Sound requires a medium to travel because it relies on particle vibrations. It cannot travel through a vacuum.

For example, when a guitar string vibrates, it pushes air particles nearby, creating compressions and rarefactions that travel through the air to your ear.

The speed and behaviour of sound waves depend on the medium they travel through, which leads us to the next section.

Speed of Sound

The speed of sound varies depending on the medium:

• Solids: Sound travels fastest because particles are tightly packed and can transmit vibrations quickly.
• Liquids: Sound travels slower than in solids but faster than in gases.
• Gases (like air): Sound travels slowest because particles are far apart.

Typical speeds of sound at room temperature (20°C) are approximately:

• Air: 343 m/s
• Water: 1480 m/s
• Steel: 5000 m/s

The speed of sound also depends on factors such as temperature and density of the medium. For example, sound travels faster in warmer air because particles move more quickly and transmit vibrations faster.

In denser materials, particles are closer together, which usually increases speed. However, if the material is very dense but particles are not tightly bonded (like some fluids), the speed can be slower.

For instance, sound travels faster through warm air than cold air, which is why you might hear sounds more clearly on a warm day.

Example: If sound travels through steel at 5000 m/s, how long does it take to travel 10 metres?

Time = distance ÷ speed = $\frac{10}{5000} = 0.002$ seconds.

Frequency, Wavelength & Pitch

The frequency of a sound wave is the number of vibrations (waves) per second, measured in hertz (Hz). Frequency determines the pitch of the sound:

• High frequency = high pitch (e.g., a whistle)
• Low frequency = low pitch (e.g., a drum)

The wavelength is the distance between two compressions or two rarefactions in the wave.

Frequency and wavelength are related by the speed of sound in the medium:

$$v = f \lambda$$

where $v$ is the speed of sound, $f$ is frequency, and $\lambda$ is wavelength.

The human ear can hear sounds in the frequency range of approximately 20 Hz to 20,000 Hz (20 kHz). Sounds above 20 kHz are called ultrasound and are inaudible to humans.

For example, a sound wave with frequency 500 Hz and speed 343 m/s in air has a wavelength:

$$\lambda = \frac{v}{f} = \frac{343}{500} = 0.686 \text{ m}$$

Reflection and Absorption of Sound

Sound waves can be reflected or absorbed when they hit a surface:

• Reflection: When sound bounces off a surface, it can create an echo. The time delay between the original sound and the echo depends on the distance to the reflecting surface.
• Absorption: Some materials absorb sound waves, reducing the amount reflected. Soft materials like carpets, curtains, and foam absorb sound well, reducing echoes and noise.

Reflection of sound is useful in applications such as:

• Echo sounding: Used by ships to measure water depth by timing echoes of sound pulses.
• Ultrasound imaging: Uses reflected sound waves to create images inside the body.
• Acoustic design: Concert halls use materials that reflect or absorb sound to improve sound quality.

Example: If an echo is heard 0.5 seconds after a sound is made, how far away is the reflecting surface? (Speed of sound in air = 343 m/s)

The sound travels to the surface and back, so the total distance is:

$$d = v \times t = 343 \times 0.5 = 171.5 \text{ m}$$

Distance to the surface is half this:

$$\frac{171.5}{2} = 85.75 \text{ m}$$