## What are sound waves?

• The vibration wave that can be heard by humans is called a sound wave, audible wave. Hertz (Hz) is the unit for the vibration frequency of sound waves, which represents the number of vibrations per second. In general, humans can hear sounds in the range from 20 Hz to 20 kHz. If the frequency of sound waves exceeds 20 kHz, then it is classified as ultrasound which our ears are unable to hear. The physical properties of ultrasound are the same as of audible sound. Sound can only propagate through a medium, such as gas, liquid or solid. Therefore, sound cannot propagate in vacuum state.
• Sound waves are longitudinal waves (compression-rarefaction wave), as shown below:
• A longitudinal wave means that the vibration of particles propagates parallel to the direction of the wave.
• When the atoms vibrate, they move back and forth around the same location. This continuous back and forth motion results in an alternating high-pressure and low-pressure regions in the medium. These high-pressure and low-pressure regions are called compressions and rarefactions, respectively. These pressure variations are transported to the surrounding medium resulting in the sound waves travelling from one medium to another.
• The speed of sound is different in different media. The speed of sound is highest in solids because the atoms in solid are highly compressed. The interaction between atoms in matter is highly dependent on the distance between particles. Higher the interaction between the atoms, quicker the transfer of the energy. As the interaction of the particles in solids is high, the speed of sound is faster than in liquids and gases. The formula used to calculate the speed of sound is given as:

c (speed of sound)=f (frequency) x λ (wavelength)

The table below lists the speed of sound in different media:

## Why do sound waves undergo attenuation, and what causes their attenuation？

A sound becomes gradually weaker during the propagation process, and this phenomenon is known as sound wave attenuation. There are three main reasons for the attenuation of sound waves:

(A)Diffusion attenuation

When sound waves propagate in all directions, their energy gradually disperses. The spreading of energy results in a reduction of the energy present per unit area, causing the perceived sound to become weaker.

(B)Absorption attenuation

When sound waves propagate through a medium, the viscosity of the medium causes internal friction between particles. As a result, some of the sound energy is transformed into thermal energy, leading to a decrease in acoustic energy and causing the perceived sound to become weaker.

(C)Scattering attenuation

When there are particulate structures present in the medium (such as suspended particles or bubbles in a liquid, tiny particles or defects in a solid), they cause the attenuation of sound waves known as scattering attenuation.

The total attenuation of the final sound wave equals the sum of diffusion attenuation (A), absorption attenuation (B), and scattering attenuation (C).

• Higher frequencies are more prone to attenuation (larger attenuation coefficients).
• Generally, the magnitude of the attenuation constant follows the following order: Solid<Liquid<Gas

## What are decibels (dB)?

• Decibels (dB) is a common unit used to measure the intensity of sound.
• The auditory range of a normal young person spans from the faintest audible sound, such as a mosquito flying 3 meters away, to extremely loud noises capable of causing hearing damage, like the sound of a ship’s engine room. The magnitudes of sound pressure values in this range can differ by up to a million times.
• The significant differences in sound pressure values mentioned above can make practical usage inconvenient. Hence, the definition of decibels (dB) was introduced.
• Where the “reference sound pressure” is the minimum sound pressure that a normal person can hear (20 µPa).
• Through the conversion of sound pressure level (dB), the vast differences spanning up to a million times mentioned earlier would fall within the range of 0 dB to 120 dB, making it more convenient for practical use.

## What are the three basic elements of sound?

The characteristics of sound can be described by three elements: Timbre、Pitch、and Loudness.

(1) Timbre→Determined by the waveform of the sound.

Timbre is related to the vibrational waveform of the sound or, in other words, the spectral structure of the sound. Our ability to distinguish between the sound of a violin and a flute, for example, is due to the differences in their waveforms (as shown in the diagram below).

(2) Pitch→Determined by the frequency of the sound.

Pitch is primarily related to the frequency of the sound waves. The higher the frequency of the sound wave (higher pitch), the higher the perceived tone. Conversely, lower frequencies (lower pitch) result in a lower, deeper sound.

(3) Loudness →The amplitude determines the loudness of the sound.
Loudness is related to the amplitude of the sound wave. In general, the greater the amplitude of the sound wave, the greater the loudness (it sounds louder).

## The fundamental parameters of sound waves:

• Sound Pressure
• This refers to the change in pressure generated by the vibration as a sound wave passes through a medium, denoted by the symbol “P”, and measured in units of N/m² (Pascal).
• Sound Pressure Level (SPL, noted by Lp) is the ratio of the actual sound pressure to the reference sound pressure, expressed as a logarithm to the base 10 and multiplied by 20. It is measured in decibels.
• Sound Intensity
• This refers to the average acoustic power per unit area passing through a point perpendicular to a certain direction within a given time interval. It is denoted by the symbol “I” and measured in units of watts per square meter (W/m²).
• Sound Intensity Level (noted by LI) is the ratio of the actual sound intensity (I) to the reference sound intensity, expressed as a logarithm to the base 10 and multiplied by 10. It is measured in decibels (dB).
• Sound Power
• The total acoustic energy emitted by a sound source per unit time. It is expressed in watts (W).
• Sound Power Level (LW) is the ratio of the actual sound power (W) to the reference power, expressed as a logarithm to the base 10 and multiplied by 10. It is measured in decibels (dB).

Where the reference values in the above equations are defined as follows:

P0: (20×10-6 N/m2)à minimum sound pressure level that a normal person can hear.

I0: 10-12 (W/m2)

W0: 10-12 (W)

The conversion calculation between sound intensity and sound pressure with distance can be performed using the following formulas.

Where I: sound intensity，P: sound pressure，ρ: medium density，c: sound velocity，r : distance away from sound source.

Based on above formulas, the following results can be deduced:

• When the distance is doubled, the sound intensity level decreases by 6 dB, and the sound pressure level (SPL) also decreases by 6 dB.
• When the sound intensity is halved, the sound pressure level (SPL) decreases by 3 dB.
• When the sound pressure is halved, the sound pressure level (SPL) decreases by 6 dB.