A wave with a constant velocity doubles its frequency. What happens to the wavelength?

The relationship between velocity, frequency and wavelength is given by: v=fλ.
In this case, we have: v=fλ₁ and v=2fλ₂ .Since the question states that the velocity is constant, we can write the equality: fλ₁=2fλ₂. Now we only have to find the relationship between λ₁and λ₂ by writing λ₂ using λ₁. We can simplify by f, and we are given λ₁=2λ₂, Divide by 2 on both sides and you find that λ₂ = λ₁/2. Use intuition by drawing a graph! It can help you understand why this phenomenon occurs.