Question

How does increasing the wavelength by 50% affect the frequency of a wave on a rope?

Answer 1

Increasing the wavelength of a rope by 50 % decreases its frequency by 33 %.

The relation between frequency and wavelength is

`fλ = v`

Then

`f_1λ_1 = f_2λ_2`

If `f_1 = f`, then `f_2 = 1.50f`

`λ_2 = λ_1 × (f_1)/(f_2) = λ_1 × f/(1.50f) = 0.67λ_1`

The new wavelength is 67 % of the original (33 % less than the original).