Increasing frequency in a given medium results in a decrease in wavelength, while the wave speed remains constant, determined by the medium's properties. The relationship between speed, wavelength, and frequency is defined by the equation speed = wavelength x frequency. When frequency is doubled, wavelength is halved, and vice versa, assuming the speed of the wave remains constant. The discussion also touches on the Doppler effect, illustrating how wave interactions change based on relative motion. Overall, frequency changes do not inherently affect wave speed but alter wavelength accordingly.