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

It decreases the frequency by 33.33%

Explanation:

The frequency of a wave is given by the division between its velocity and its wavelength:

f = v/L, where f is the frequency in hertz, v is the velocity in m/s, and L is the wavelength in meter

If we increase the wavelength by 50 percent, we have that L' = 1.5*L (L' is the new wavelength)

Keeping the same velocity, we have the new frequency (f') as:

f' = v/L' = v/1.5*L = (1/1.5) * v/L = 0.6667*f

The new frequency is 66.67% of the old frequency, that is, the old frequency decreased 33.33%.

So, increasing the wavelength by 50% decreases the frequency by 33.33% or 1/3