Question

String $1$ is connected with string $2$. The mass per unit length in string $1$ is ${\mu }_1$ and the mass per unit length in string $2$ is $4{\mu }_1$. The tension in the strings is $T$. A travelling wave is coming from the left. What fraction of the energy in the incident wave goes into string $2$?

• A. $1/8$
• B. $4/9$
• C. $2/3$
• D. $8/9$

Answer 1

The correct option is D $8/9$

Let $v_1$ and $v_2$ are the velocities of the waves in string 1 and string 2 respectively

$v_1=\sqrt{\frac{T}{{\mu }_1}}$ $v_2=\sqrt{\frac{T}{4{\mu }_1}}$ $v_1=2v_2$

Then the energy reflected in string 1 will be

$A_{reflected}=\left(\frac{2v_2}{v_1+v_2}\right)A_{incident}$

$E_{reflected}=\frac{1}{3}{E}_{incident}$

$E_{transfered}=\frac{8}{9}{E}_{incident}$