Question

How does the increase of wavelength by 50% affect the frequency of a wave that travels in a rope?

Answer 1

The relationship between the frequency and the wavelength of the wave can be written as follows:

$$f\lambda=v.$$

From this formula we can find the frequency of the wave:

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

Let the wavelength increases by 50%, then we can write:

$$f_{new}=\dfrac{v}{1.5\lambda}=\dfrac{f}{1.5}=0.67f.$$

As we can see from the calculations, the new frequency is 67% of the old frequency. In other words, the old frequency decreases by 33%.

Answer:

If the wavelength of the wave increases by 50% the frequency of the wave decreases by 33%.