What happens to wave speed if the frequency is increased while keeping the wavelength constant?

In wave physics, the relationship between wave speed, frequency, and wavelength is given by the equation:

[ \text{Wave Speed} = \text{Frequency} \times \text{Wavelength}

]

If the wavelength is held constant and the frequency is increased, the equation shows that the wave speed must also increase. This is because wave speed is directly proportional to frequency when wavelength is fixed. Therefore, if you increase the frequency while keeping the wavelength unchanged, the product of frequency and wavelength (which determines the wave speed) results in a higher wave speed.

For instance, if you consider a wave in a medium where the distance between the peaks (wavelength) remains the same, but you have more peaks passing a certain point per unit time (increased frequency), it means that the energy and information carried by the waves are being transmitted more rapidly through that medium. Hence, the wave speed increases as stated by the equation.

Other options, such as the speed remaining the same or decreasing, don't align with this fundamental wave relationship, and suggesting the speed becoming zero does not apply since a wave would not propagate without a speed.