No, the speed of a sound wave does not change if its frequency increases. The speed of sound in a given medium is determined by the properties of that medium, such as its density and elasticity. It is not directly influenced by the frequency of the sound wave.
The frequency of a sound wave refers to the number of cycles or vibrations per unit of time. As the frequency increases, the wavelength decreases (since wavelength is inversely proportional to frequency), but the speed of sound in the medium remains the same.
This can be understood using the wave equation: speed = frequency × wavelength. If the frequency increases while the speed remains constant, the wavelength must decrease proportionally to compensate and satisfy the equation.
In summary, while the frequency and wavelength of a sound wave are related, the speed of sound itself does not change with a change in frequency.