A string of length 100 ~cm has three resonant frequencies, 120 ~Hz , 200 ~Hz and 280 ~Hz . If a node is formed at the end of the string, the speed of the transverse wave on this string is :

Step-by-step solution

Given, length of string, l=100 ~cm =1 ~m Three resonant frequencies are given as f₁=120 ~Hz , f₂=200 ~Hz , f₃=280 ~Hz Fundamental frequency (f₀ ) is equal to the greatest common factor of f₁, f₂ and f₃ . f₀= greatest common factor of 120 ~Hz , 200 ~Hz and 280 ~Hz i.e., f₀=40 ~Hz Now, we know that, speed of transverse wave is given by v=2 l f₀=2 1 40=80 ~m / s .