Question

For the speed of a transverse wave on a string , we write the formula v = √(T/μ) and sometimes we also we also write v = fλ. Are these two same or different ? Explain.

Answer 1

Speed of a wave depends on some special characteristics of the medium. For Problem, in case of a string it depends on T and μ. Frequency f depends on the source. Wavelength is self adjusted (= v/f). 

Let us take an Problem.

Suppose tension in a string is 100 N, linear mass density (μ) of this wire is 1 kg/m. Then in such a string speed of the transverse wave is ,

This value of 10 m/s is now fixed under the given conditions (T = 100 N, μ = 1 kg/m). Now suppose we keep the frequency of a a wave 10 Hz, then wavelength of such a wave will become 1 m (= v/f) . Now if frequency is reduced to 5 Hz (half), the wavelength will become two times or 2 m, so that product of λ and f remains constant (= 10 m/s)