The fundamental frequency of sound waves in air refers to the lowest frequency at which a standing wave can be formed in a given medium. In the case of air, the fundamental frequency of sound waves is determined by the speed of sound in air and the length of the resonating medium.
The speed of sound in air depends on various factors such as temperature, humidity, and composition. However, at room temperature and normal atmospheric conditions, the approximate speed of sound in dry air is around 343 meters per second (m/s) or 767 miles per hour (mph).
The fundamental frequency (f) of a standing wave in a resonating medium, such as an open or closed tube, can be determined using the following formula:
f = v / λ
where v is the velocity of sound in air and λ is the wavelength of the standing wave. For a resonating tube, the length of the tube plays a role in determining the wavelength and, consequently, the fundamental frequency.
For example, in an open tube (like an open pipe or an open end of a flute), the fundamental frequency corresponds to the wavelength that is twice the length of the tube. Therefore, the fundamental frequency (f₁) can be expressed as:
f₁ = v / (2L)
where L is the length of the tube.
In a closed tube (like a closed pipe or the closed end of a flute), the fundamental frequency corresponds to the wavelength that is four times the length of the tube. Hence, the fundamental frequency (f₁) in a closed tube can be expressed as:
f₁ = v / (4L)
The harmonic analysis of sound waves in air involves studying the higher frequencies present in addition to the fundamental frequency. Harmonics are integer multiples of the fundamental frequency and are also known as overtones. They contribute to the characteristic timbre or quality of a sound.
For example, if the fundamental frequency of a sound wave is 100 Hz, the first harmonic or the second overtone would be 200 Hz, the second harmonic or the third overtone would be 300 Hz, and so on. The amplitudes and relative strengths of these harmonics determine the specific sound produced by an instrument or a source.
In summary, the fundamental frequency of sound waves in air depends on the speed of sound and the length of the resonating medium. The harmonic analysis of sound waves involves studying the additional frequencies that are integer multiples of the fundamental frequency, known as harmonics or overtones.