A string 120 cm in length sustains standing wave with the points of the string at which the displacement amplitude is equal to 3.5 mm being separated by 15.0 cm. The maximum displacement amplitude is X. 95 mm then find out the value of X.

Explanation

In this problem two cases are possible

Case-I is that A and B have the same displacement amplitude and Case-2 is that C and D have the same amplitude viz 3.5 mm. In case 1, if x = 0 is taken at antinode then
A = a cos kx In case -2, if x = 0 is taken at node, then A = a sin kx But since nothing is given in the question. Hence from both the cases, result should be same. This is possible only when a cos kx = a sin kx

or `kx=(pi)/4 or a=(A)/(coskx)=(3.5)/(cospi//4)=4.95 mm`