Question

What happens to the wavelength of a wave on a string when the frequency is doubled

Answer 1

Answer:

$\lambda'=\dfrac{1}{2}\times \lambda$

Explanation:

The number of oscillation per unit time is called frequency of a wave while the distance between two consecutive crests and the trough is called its wavelength.

The wavelength of a wave is given by :

$\lambda=\dfrac{v}{f}$

If frequency is doubled, f' = 2f

$\lambda'=\dfrac{v}{f'}$

$\lambda'=\dfrac{v}{2f}$

$\lambda'=\dfrac{1}{2}\times \dfrac{v}{f}$

$\lambda'=\dfrac{1}{2}\times \lambda$

So, when the frequency is doubled the wavelength of a wave on the string becomes half.