Final answer:
If the frequency of a wave is doubled, its wavelength is halved and its period is also halved, assuming the wave speed remains constant.
Step-by-step explanation:
If the frequency of a wave is doubled, keeping the wave speed constant, the resulting wavelength will be halved, since the wavelength is inversely proportional to the frequency. The wave equation, which is velocity (v) = frequency (f) × wavelength (λ), illustrates this relationship. Therefore, if the frequency is doubled (f becomes 2f), we can express the new wavelength (λ') as λ/2 because v = fλ = 2f(λ/2).
As for the period (T) of the wave, which is the inverse of the frequency, if the frequency is doubled, the period is halved. The period can be calculated using the formula T = 1/f. Therefore, when the frequency is doubled, the new period (T') will be T/2.