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.
