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

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Answer 1 · 2015-03-30T00:15:09

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).