Question

I have a question,
how come speed of a wave in an ideal string is independent of frequency when v=lambda*frequency?

Answer 1

As the frequency varies in the string, the wavelength will vary in inverse proportionality. Hence, lamda*frequency will have a constant value which is equal to V, the velocity of the wave. Try making lamda the subject of the equation and plug in different values for frequency, keeping the velocity the same. You will get a range of values for both frequency and wavelength which will satisfy the original equation for a constant speed.