Question

String #1 is connected with string #2. The mass per unit length in string #1 is 1 and the mass per unit length in string #2 is 4 1. The tension in the strings is t. A traveling wave is coming from the left. What fraction of the energy in the incident wave goes into string #2 ?

Answer 1

which class question is this ??

Answer 2

The fraction of energy in incident was is 8/9.

Let the mass per unit length of first string = u1

Let the mass per unit length of second string =   4u1

Tension acting on the string = T

Impedence of first string = √u1T

Impedence of second string = √4u1T

When intensity is transmitted -

T = 4z1z2( z1+z2)²

T = 4 × √u1T × √4u1T ( √u1T + √4u1T)²

T = 4u1T ×√4/ u1T ( 1 + √4)²

T = 4 ×√4/ ( 1 + √4)²

= 8/9

Therefore, the fraction of energy in incident was is 8/9.