Final answer:
The second sound wave, with twice the frequency of the first, will have a wavelength that is half that of the first wave, while the speed of the wave remains the same in the same medium.
Step-by-step explanation:
When considering a sound wave's travel through water, we rely on the fundamental wave relationship given by v = fλ, which states that the speed (v) of the wave is equal to the product of its frequency (f) and wavelength (λ). Considering a second sound wave with twice the frequency of the first and traveling through the same medium (water), we can infer that the speed of the wave will remain the same, as the speed of sound is nearly independent of frequency in a given medium.
In this case, if we denote the first wave's frequency as f and its wavelength as λ, the second wave's frequency would be 2f. Since the speed of sound in water does not change (because the medium has not changed), we must adjust the wavelength to maintain the relationship v = fλ. For the second wave, the equation will be v = 2fλ2, where λ2 is the new wavelength.
Since the speed of sound v is constant, we can deduce that λ2 must be half the value of the original wavelength (λ) to compensate for the doubled frequency. Therefore, the wavelength of the second wave is half that of the first wave, while the speed of the wave remains unchanged.