"If you double the wavelength of a wave on a particular string", what happens to the wave speed v and the frequency f ? (i) v do
ubles and f is unchanged; (ii) v is unchanged and f doubles; (iii) v becomes onehalf as great and f is unchanged; (iv) v is unchanged and f becomes one-half as great; (v) none of these. â
Velocity is directly proportional to wavelength. Direct proportionality shows that increase in velocity will cause an increase in the wavelength and decrease in velocity will also cause a decrease in wavelength with the frequency not changing since the velocity and wavelength are both increasing and decreasing at the same rate.
According to the question, if the wavelength is doubled, the velocity (v) will also double while the frequency (f) remains unchanged.
The relationship between wave speed (v), frequency (f) and wavelength (λ) of a string wave is given by;
v = f x λ
As seen, the wave speed is directly proportional to the frequency provided the wavelength remains constant. Also, if frequency is left constant, the wave speed will be directly proportional to the wavelength. Also the frequency increases as wavelength decreases and vice-versa while the speed remains constant.
Therefore, when the wavelength is doubled, the wave speed will also be doubled while frequency remains unchanged.
