The string of length 2 ~m is fixed at both ends. If the string vibrates in its fourth normal mode with a frequency of 500 ~Hz , then the waves would travel on it with a velocity of

Step-by-step solution

The frequency of the n -th normal mode of a string of length L fixed at both ends is given by f_n = n v 2L , where v is the wave velocity. Given L = 2 m , n = 4 , and f₄ = 500 Hz . Substituting the values into the formula: 500 = 4 v 2 2 500 = 4v 4 v = 500 m/s Answer: 500 ~m / s