Sound waves are often represented as sinusoidal waves because they can be described mathematically using sine or cosine functions. However, it's important to note that sound waves in the real world can be more complex and contain various frequencies and amplitudes.
The reason sinusoidal waves are commonly used to describe sound waves is based on the understanding that many sounds can be broken down into a combination of pure tones or sine waves of different frequencies and amplitudes. This concept is known as Fourier analysis or spectral decomposition.
According to Fourier analysis, any complex sound wave can be represented as a sum of individual sine waves with different frequencies, amplitudes, and phases. This is known as the Fourier series or Fourier transform. By analyzing the different components of a sound wave, it becomes possible to understand its frequency content, harmonics, and overall characteristics.
Sinusoidal waves are mathematically convenient because they have a simple waveform, characterized by a repetitive pattern with a single frequency. They can be easily described using mathematical equations and manipulated using various mathematical operations.
In reality, sound waves produced by most sources, such as musical instruments, voices, or environmental noises, are not perfectly sinusoidal. They are often complex waveforms with multiple frequencies and harmonics. However, by using Fourier analysis, these complex waveforms can be broken down into their constituent sinusoidal components, allowing us to analyze and understand the properties of the sound.
So, while sound waves can be more complex than simple sine waves, the sinusoidal representation is a useful mathematical tool for understanding and analyzing sound.