Transmission of 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 around it to vibrate too, creating regions of compression (particles close together) and rarefaction (particles spread apart).

Sound waves require a medium to travel through, such as air, liquids, or solids. They cannot travel through a vacuum because there are no particles to vibrate and carry the wave.

The particles themselves do not travel with the wave; instead, they oscillate back and forth about their fixed positions, passing the energy along.

For instance, when you speak, your vocal cords vibrate, causing air particles to vibrate in a longitudinal wave that travels through the air to the listener’s ear.

Transmission in Solids, Liquids & Gases

Sound waves travel through solids, liquids, and gases, but the speed of transmission depends on how closely packed the particles are in the medium:

• Solids: Particles are very close together and strongly bonded. This allows vibrations to pass quickly from particle to particle, so sound travels fastest in solids.
• Liquids: Particles are less tightly packed than solids but closer than gases. Sound travels slower than in solids but faster than in gases.
• Gases: Particles are far apart and move freely. Sound travels slowest in gases because particles take longer to pass vibrations along.

For example, sound travels through steel at about 5000 m/s, through water at about 1500 m/s, and through air at about 343 m/s (at 20°C). These values are approximate and can vary with temperature, pressure, and the purity of the medium.

Wave Propagation Mechanism

Sound waves propagate by particles oscillating around their equilibrium positions:

• Particle oscillation: Each particle vibrates back and forth in the direction of the wave.
• Energy transfer: Energy moves through the medium as particles push and pull on their neighbours, but particles themselves do not travel along the wave.
• Compression and rarefaction: The wave consists of alternating compressions (high pressure) and rarefactions (low pressure) that move through the medium.

This oscillation causes the pressure variations that our ears detect as sound.

For example, when a speaker cone moves forward, it compresses air particles in front of it (compression). When it moves back, it creates a region where particles are more spread out (rarefaction). These pressure changes travel through the air as a sound wave.

Factors Affecting Transmission

Several factors affect how sound waves transmit through a medium:

• Medium density: Denser media usually transmit sound faster because particles are closer and interact more quickly. However, if the medium is too dense and particles are heavy, this can slow sound down.
• Temperature: Higher temperatures increase the energy of particles, making them vibrate faster and transmit sound waves more quickly. For example, sound travels faster on a warm day than on a cold day.
• Impedance mismatch: When sound passes from one medium to another with very different densities (or acoustic impedances), some sound is reflected and some transmitted. This reflection occurs because the difference in acoustic impedance causes part of the wave energy to bounce back, reducing the amount of sound energy passing through the boundary.

For example, when sound travels from air into water, much of it is reflected because of the large difference in density, so only some sound energy passes into the water.

Example: Calculating the speed of sound in air at different temperatures

The speed of sound in air increases by about 0.6 m/s for every 1°C rise in temperature above 0°C. At 0°C, the speed of sound is approximately 331 m/s.

Calculate the speed of sound in air at 20°C.

Using the formula:

$$v = 331 + (0.6 \times T)$$

where $T$ is temperature in °C.

Substitute $T = 20$:

$$v = 331 + (0.6 \times 20) = 331 + 12 = 343 \text{ m/s}$$

So, the speed of sound at 20°C is 343 m/s.