Question

If the velocity and frequency of a wave are both doubled, how does the wavelength change?

Answer 1

Answer:

the wavelength increases

Explanation:

Answer 2

The wavelength will remain unchanged.

Explanation:

The velocity $v$ of a wave in terms of its wavelength $\lambda$ and frequency $\nu$ is

$v = \lambda\nu$ (1)

so if we double both the velocity and the frequency, the equation above becomes

$2v = \lambda(2\nu)$ (2)

Solving for the wavelength from Eqn(2), we get

$\lambda = \dfrac{2v}{2\nu} = \dfrac{v}{\nu}$

We would have gotten the same result had we used Eqn(1) instead.