# Introduction to Sound Waves

This topic is part of the HSC Physics course under the section Sound Waves.

### HSC Physics Syllabus

• conduct a practical investigation to relate the pitch and loudness of a sound to its wave characteristics
• model the behaviour of sound in air as a longitudinal wave
• relate the displacement of air molecules to variations in pressure (ACSPH070)
• conduct investigations to analyse the reflection, diffraction, resonance and superposition of sound waves (ACSPH071)

### What is Sound?

Sound is a mechanical wave that requires a medium to propagate and transfer energy (like air, water, or solid materials) It arises from the vibrations of an object, which then causes the surrounding medium's particles to vibrate in kind.

Unlike transverse waves, where the medium's displacement is perpendicular to the wave's direction, sound waves are longitudinal waves. In these waves, the medium's particles move parallel to the direction of wave propagation. This movement leads to areas of compression (where particles are close together) and rarefaction (where they are spread apart).

When a sound wave propagates through air, compression and rarefaction also correspond to points of high and low air pressure respectively.

### Properties of Sound

• Frequency: Measured in Hertz (Hz), it defines the number of vibrations per second. High-frequency sounds are high-pitched, while low frequencies sound low. The human ear can generally detect sounds in the range of 20 Hz to 20,000 Hz.

• Amplitude: Represents the maximum displacement of vibration caused by sound wave it propagates through a medium. The amplitude determines the sound's "loudness" or volume. Greater amplitude means a louder sound.

• Wavelength: The distance between two consecutive compressions or rarefactions.

• Speed: The speed at which sound travels depends on the medium. For instance, in dry air at 25°C, sound travels at approximately 340 m/s. This speed is faster in water and even faster in solid materials due to tighter particle arrangements.

### Factors That Affect The Speed of Sound

Sound waves are mechanical waves whose velocity depends on various factors.

• Medium: sound waves travel faster in solids than in gaseous media. This is because atoms are more tightly compacted in solid states compared to gas. When a sound wave is transmitted through a solid medium, energy transfer due to the vibration of adjacent atoms allows for a faster transmission.

• Temperature: sound waves travel faster at a higher temperature. For example, sound waves travel faster in air when the temperature of air is higher. This is because gas molecules have more kinetic energy (greater velocity) at a higher temperature, resulting in more collision and thus transfer of energy between air molecules.

• Altitude: the speed of sound waves in air depends on its pressure. Air pressure decreases with increasing altitude. Therefore, sound waves travel slower at higher altitudes due to fewer collision and slower transfer of energy between air molecules.

• Humidity of air: air with greater humidity has a greater proportion of water molecules. Since water molecules have smaller molecular mass compared to oxygen and nitrogen gas, as humidity increases, the average molecular weight of air decreases.  In a medium with lighter molecules, sound waves can propagate more quickly. Therefore, sound travels faster in more humid air compared to dry air.

### Behaviour of Sound Waves

Sound waves exhibit basic behaviours of all waves including reflection, refraction, and diffraction.

• Reflection: Just as light waves reflect off surfaces, sound waves can too. This phenomenon is responsible for echoes.

• Refraction: Sound waves can bend when they move from one medium to another, due to a change in speed. When sound waves enter a new medium, their frequency and as a result, velocity change.

• Diffraction: When sound waves encounter an obstacle or opening, they can bend around or spread out. It's why you can still hear someone's voice even if they are behind a wall.

### Resonance in Sound Waves

When it comes to sound, resonance occurs in air columns, stringed instruments, and many other objects. For instance:

1. Air Columns: Wind instruments, like flutes or organs, have air columns that vibrate at specific frequencies. When a musician plays a note that matches one of these frequencies, the instrument resonates, producing a loud, clear note. This is discussed separately here

2. Stringed Instruments: In guitars or violins, plucking a string makes it vibrate at its natural frequency. The body of the instrument then resonates with this frequency, amplifying the sound. This is discussed separately here.

Resonance can also lead to the amplification of sound waves in certain environments, such as an empty room echoing a particular frequency more than others.

### Superposition in Sound Waves

The principle of superposition states that when two or more waves meet, the resultant wave is the algebraic sum of their individual amplitudes. This is discussed in greater detail here.

1. Constructive Interference: When two sound waves meet and are in phase (their compressions and rarefactions align), their amplitudes add together. This results in a louder sound. It's called constructive interference because the waves build upon or "construct" each other.

2. Destructive Interference: When two sound waves are out of phase (a compression of one meets a rarefaction of the other), they can cancel each other out. If two waves are perfectly out of phase and have equal amplitudes, they will completely negate each other, producing no sound. This is the principle behind noise-cancelling headphones.

3. Partial Interference: In real-world scenarios, waves rarely meet perfectly in or out of phase. They often partially construct or destruct each other, leading to varied resultant amplitudes.

#### Example of Sound Superposition in Everyday Life

Noise cancelling technology, particularly in headphones, works by using the principles of sound interference and superposition. Noise-cancelling headphones use microphones to detect ambient sounds. Once the external sound is detected, the headphones' internal electronics create a sound wave that is the exact opposite (180 degrees out of phase) of the detected noise. This new sound wave is known as "anti-noise." When the anti-noise is played through the headphones' speakers, it meets with the external noise and undergoes destructive interference. The outcome of this destructive interference is a significant reduction in the volume of the external noise heard by the listener. In essence, the noise and anti-noise cancel each other out, leading to a quieter or even silent listening experience.