Question

Two strings with mass per unit length of $25 \, g \, cm^{-1}$ and $9 \, gcm^{-1}$ are joined together in series. The reflection coefficient for the vibration waves are

• A. $\frac{9}{25}$
• B. $\frac{3}{5}$
• C. $\frac{1}{16}$
• D. $\frac{9}{16}$

Answer 1

Answer: (C)

$\frac{1}{16}$

Answer 2

Let $I_r$ and $I_i$represent the intensities of reflected and incident waves respectively, then
\hspace30mm \frac{I_r}{I_i} = \big(\frac{\mu - 1}{\mu + 1}\big)^2
where \hspace20mm \mu = \frac{v_1}{v_2} \, or \, v = \frac{\sqrt{\frac{T}{m_1}}}{\sqrt{\frac{T}{m_2}}} = \sqrt{\frac{m_2}{m_1}} = \sqrt{\frac{25}{9}} = \frac{5}{3}

\therefore \hspace20mm \frac{I_r}{I_i} = \Bigg [\frac{\big(\frac{5}{3}\big) - 1}{\big(\frac{5}{3}\big) + 1}\Bigg ]^2 = \frac{1}{16}