Physics of Sound: Concepts, Intensity, and Doppler Effect
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Sound: Concepts and Characteristics
In physics, sound is defined as a periodic perturbation in air. It is a mechanical longitudinal wave, where the motion of particles in the medium travels in the same direction as the wave, which propagates through an elastic medium. This periodic perturbation originates sound waves.
For sound to be produced, there must be vibrating matter and an elastic medium. For example, a guitar's vibrating strings produce sound.
Speed of Sound
The speed of sound (v) is calculated depending on the medium of propagation. In air, its speed is 331 m/s at 0°C and 1 atm. To estimate the speed of sound in air at different temperatures, the following formula is used:
Where temperature is measured in °C.
Speed of Sound in Various Materials
Table 4.1: Speed of sound in different materials:
| Material | Speed (m/s) |
| Air (20ºC) | 331 |
| Hydrogen | 1300 |
| Water | 1440 |
| Salt Water | 1560 |
| Iron | 5000 |
| Wood | 4000 |
Sound Intensity and Level
Sound Intensity
Sound intensity (I) is the power transferred by the wave through a normal area in the direction of propagation. Its units are watts per square meter (W/m²).
Sound Level (Decibels)
Once sound intensity has been defined, we can introduce the sound level (β), which is measured in decibels (dB) and follows the following relation:
 | Where
|
is the minimum audible intensity.
Audible Range, Ultrasound, and Infrasound
The audible range for human hearing typically spans from approximately 20 Hz to 20,000 Hz.
When sound exceeds the maximum audible frequency, it is called ultrasound. Conversely, when it is below the minimum audible frequency, it is known as infrasound. In both these cases, human hearing cannot perceive the sounds produced.
Example: Calculating Sound Intensity
At an outdoor party, the sound level is 120 dB. What is the sound's intensity?
From the previous equation, we can solve for the sound intensity I:
The Doppler Effect
The Doppler effect is the apparent change in frequency of a wave when there is relative motion between the sound source and the listener. For example, when an ambulance drives by with its siren on, as it moves closer, the sound becomes higher pitched (due to a shorter wavelength). As it moves away, the sound becomes lower pitched (due to a longer wavelength).
Doppler Effect Formulas
For a Still Source
Where 
is the speed of sound and 
is the frequency of the source.
For a Moving Source
Where vs is the speed at which the source moves closer or further.
Where f' is the frequency perceived by the listener.
Example: Doppler Effect Calculation
A motionless observer is near a railway where the temperature is 0°C. A train approaches at 120 m/s, and its whistle has a 500 Hz frequency. What frequency would the listener hear as the train approaches?
Using the appropriate formula, we calculate:
