Question

A wave is travelling from heavier string to a lighter. If the ratio of wavelength of incident to transmitted wave is $1:4$, then the ratio of the linear mass density of heavier string to the lighter string is

• A. $1:4$
• B. $4:1$
• C. $1:16$
• D. $16:1$

Answer 1

The correct option is D $16:1$


We know frequency (f) will remain same for incident as will as tranmitted wave
$\therefore f=\frac{V_i}{{\lambda }_i}=\frac{V_t}{{\lambda }_t}$
where ${\lambda }_i$ = wavelength of incident wave
${\lambda }_t$ = wavelength of transmitted wave
Given : $\frac{{\lambda }_i}{{\lambda }_t}=\frac{1}{4}$
$\Rightarrow f=\frac{V_i}{V_t}=\frac{{\lambda }_i}{{\lambda }_t}=\frac{1}{4}$
Using $V=\sqrt{\frac{T}{\mu }}$
$\Rightarrow \frac{\sqrt{\frac{T}{{\mu }_1}}}{\sqrt{\frac{T}{{\mu }_2}}}=\frac{{\lambda }_i}{{\lambda }_t}=\frac{1}{4}$
$\Rightarrow \sqrt{\frac{{\mu }_2}{{\mu }_1}}=\frac{1}{4}\Rightarrow \frac{{\mu }_2}{{\mu }_1}=\frac{1}{16}$
$\Rightarrow \frac{{\mu }_1}{{\mu }_2}=\frac{16}{1}$