A piano wire A vibrates with a fundamental frequency of 600 Hz . A second identical wire B generates 6 beats per second with it when the tension in A is slightly increased. Determine the ratio of the tension in A to the tension in B .

Step-by-step solution

The initial fundamental frequency of wire A and the identical wire B is f_B = 600 Hz . When the tension in wire A is slightly increased, its frequency increases. Since it produces 6 beats per second with wire B, the new frequency of wire A is: f_A = 600 + 6 = 606 Hz The fundamental frequency of a stretched string is given by f = 1 2L T , which implies f T . Therefore, the ratio of the tension in A to the tension in B is: T_A T_B = ( f_A f_B )^2 T_A T_B = ( 606 600 )^2 = (1.01)^2 = 1.0201 1.02