If the frequency of a wave doubles, what happens to the wavelength?

When the frequency of a wave doubles, the wavelength decreases by one half due to the inverse relationship between frequency and wavelength defined by the equation:

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

In this equation, the speed of sound in a given medium is constant. If the frequency increases, the wavelength must decrease to maintain the constant speed. Specifically, since frequency is inversely proportional to wavelength, when the frequency doubles, the wavelength must become half of its original length to satisfy the relationship. This fundamental principle is crucial in understanding wave behavior in mediums, particularly in ultrasound contexts where frequency adjustments can significantly impact image resolution and penetration depth.