In a given medium, the speed of sound remains relatively constant regardless of the frequency of the sound wave. This phenomenon is known as the "independence of frequency and speed" in a medium. The reason for this lies in the nature of sound propagation and the properties of the medium.
When a sound wave travels through a medium, it does so by causing a series of compressions and rarefactions in the particles of the medium. These regions of high pressure (compressions) and low pressure (rarefactions) propagate as the wave moves through the medium. The speed of sound is determined by the characteristics of the medium, such as its density, elasticity, and temperature.
Different frequencies of sound waves correspond to different numbers of compressions and rarefactions occurring per unit of time. Higher-frequency sound waves have more cycles per second (measured in Hertz) compared to lower-frequency sound waves. However, despite the variation in the number of compressions and rarefactions, the speed at which these regions of compression and rarefaction travel through the medium remains constant.
To understand this, consider a simple analogy with a line of people holding hands. If each person in the line starts shaking their hand up and down at different frequencies, the speed at which the wave of hand movements travels along the line will be the same, regardless of the frequency at which each person shakes their hand. Similarly, in a sound wave, the individual particles in the medium move back and forth, creating regions of compression and rarefaction that propagate at the same speed.
In summary, the speed of sound in a medium is determined by the properties of the medium itself and remains constant regardless of the frequency of the sound wave. The variation in frequency affects the number of compressions and rarefactions per unit of time but does not impact the speed at which these regions propagate through the medium.