1.1 Properties of Sound

 

a) Frequency

 

Frequency (ƒ) is the number of wave cycles per second and is measured in Hertz (Hz).

Frequency formula:

where T is the period, or the time it takes for one complete cycle, in seconds.

Practical example: If a wave has a period of 0.01 seconds, its frequency will be:

 

This means the wave completes 100 cycles per second.

Frequency is related to the perceived pitch: higher frequencies produce high-pitched sounds, while lower frequencies produce low-pitched sounds. In sound systems:

Low frequencies (20 to 250 Hz) correspond to bass.
Mid frequencies (250 to 4000 Hz) correspond to voices and mid-range instruments.
High frequencies (4000 to 20,000 Hz) correspond to treble.

 

b) Amplitude

 

Amplitude is related to sound pressure or sound intensity. A greater wave amplitude corresponds to a louder or more intense sound.

Sound intensity (I) is defined as power per unit area, measured in W/m2 (watts per square meter).

Sound intensity formula:

where P is power in watts and A is the area in square meters through which the sound is distributed.

The relationship between sound intensity and perceived loudness is logarithmic. The intensity and sound pressure levels are expressed in decibels (dB), as explained later.

 

 

c) Wavelength

 

Wavelength (λ) is the distance between two equivalent points in a wave cycle (e.g., crest to crest or trough to trough).

Wavelength formula:

where v is the speed of sound in the medium and ƒ is the wave frequency.

Practical example: In air at 20 °C, the speed of sound is approximately 343 m/s. For a sound with a frequency of 100 Hz:

This wavelength is typical for low-frequency sounds. Higher frequencies result in shorter wavelengths.

 

 

d) Speed of Sound

 

The speed of sound (v) depends on the medium through which it propagates. In air at 20 °C, it is approximately 343 m/s, but it varies with temperature and medium density.

Speed of sound formula in air:

where T is the temperature in degrees Celsius.

Example: At 30 °C, the speed of sound is:

The speed of sound is crucial for synchronizing speaker systems in large venues, as sound can take time to reach distant areas.

 

 

1.2 Basic Principles of Acoustics

 

a) Sound Reflection

 

Reflection occurs when a sound wave encounters a surface and bounces back. The amount of reflection depends on the angle of incidence and the surface’s characteristics.

Law of reflection: The angle of incidence equals the angle of reflection.

Example: A smooth, hard wall reflects more sound than a wall with absorbent materials. This is important in spaces like auditoriums, where reflections are controlled to avoid echo and improve sound clarity.

 

 

b) Sound Absorption

 

Absorption is the loss of sound energy when a wave hits a surface, converting it into heat.

Absorption coefficient (αα) indicates the amount of sound absorbed, ranging from 0 (no absorption) to 1 (total absorption).

Absorption formula in dB:

 

where Iincident is the sound intensity before hitting the surface and Itransmitted​ is the intensity after absorption.

Materials like carpets and acoustic panels have high absorption coefficients and are used to reduce reverberation.

 

 

c) Sound Diffusion

 

Diffusion scatters sound waves in multiple directions, softening concentrated reflections and creating a uniform sound field.

Diffusers have irregular shapes or grooves that disperse sound instead of reflecting it in a single direction.

Practical example: In recording studios, diffusers are placed on walls or ceilings to prevent wave buildup and improve sound quality.

 

 

d) Sound Refraction

 

Refraction occurs when sound changes direction as it passes through a medium with different density or temperature.

Snell’s Law for refraction:

where θ1 and θ2​ are the angles of incidence and refraction, and v1​ and v2​ are the sound speeds in each medium.

This phenomenon is common outdoors, where temperature variations can bend sound upward or downward, affecting propagation during outdoor events.

 

 

1.3 Common Acoustic Phenomena in Enclosed Spaces

 

a) Reverberation

 

Reverberation is the persistence of sound in a space after the source has stopped, caused by multiple reflections on surfaces.

Reverberation Time (RT60): The time it takes for sound to decay by 60 dB after the source stops.

Sabine formula:

where V is the volume of the space in cubic meters and A is the total absorption in square meters.

 

 

b) Echo

 

An echo is a type of reflection where sound arrives with a noticeable delay. It is perceived when the distance between the listener and the reflective surface causes a delay of at least 50 ms.

Example: In large auditoriums, echo is minimized by adjusting speaker placement and using absorbent materials.

 

 

c) Room Modes

 

Room modes are specific frequencies that resonate in enclosed spaces due to reflections between parallel walls. These create areas of high and low sound pressure.

Axial mode frequency formula:

where L is the distance between parallel surfaces, and v is the speed of sound.

Room modes mainly affect low frequencies and are controlled using bass traps or redesigning room dimensions.

 

 

1.4 Concepts of Decibels (dB) and Sound Pressure Level (SPL)

 

a) Decibels (dB)

 

Decibels are a logarithmic unit measuring relative sound intensity.

Decibel formula:

where I is the sound intensity, and I0​ is the reference intensity (commonly 10−12 W/m210−12W/m2 for the threshold of hearing).

 

 

b) Sound Pressure Level (SPL)

 

SPL measures sound pressure in dB at a specific point and is used in live settings to ensure safe and appropriate volume levels.

SPL formula:

where p is the sound pressure in pascals, and p0​ is the reference pressure (20 μPa).

With these principles and formulas, sound behavior in different spaces can be analyzed and adjusted to achieve optimal audio quality.