Question

A string consists of two parts attached at x = 0. The right part of the string (x > 0) has mass ${\mu }_r$ per unit length and the left part of the string (x < 0) has mass ${\mu }_l$ per unit length. The string tension is T. If a amplitude of the wave that is transmitted to the right part of the string?
$\to {\mu }_l{\mu }_r$

• A. 1
• B. $\frac{2}{1+\sqrt{{\mu }_l/{\mu }_r}}$
• C. $\frac{2\sqrt{{\mu }_l/{\mu }_r}}{1+\sqrt{{\mu }_l/{\mu }_r}}$
• D. $\frac{2\sqrt{{\mu }_l/{\mu }_r}-1}{1+\sqrt{{\mu }_l/{\mu }_r}+1}$

Answer 1

The correct option is B $\frac{2}{1+\sqrt{{\mu }_l/{\mu }_r}}$

Trassmisibility of a transverse wave by in given by

$tr=\frac{y_r}{y}=\frac{2k_r}{k_L+k_r}$

$y_r,y_r$ are amplitude of pulses in right

and left string respectively

also,$k_r{k}_L$ are wave number $(=\frac{2\pi }{\lambda })$ of the wave

$\mu$ : linear man density of string.

In this case $\lambda \alpha \sqrt{\mu }$

So, $tr=\frac{2}{\frac{k_1}{k_r}+1}$

that gives,

$t_r=\frac{y_r}{y_r}=\frac{2}{\left(\sqrt{{\mu }_r/{\mu }_r}\right)+1}$ (Ans)