Question

A wave travelling on a string is transmitted to other string of different density, gets partially reflected at the junction. The reflected wave is inverted in shape as compared to the incident wave. If the incident wave has wavelength ${\lambda }_1$ and the transmitted wave ${\lambda }_2,$ then

• A. ${\lambda }_2>{\lambda }_1$
• B. ${\lambda }_2={\lambda }_1$
• C. ${\lambda }_2<{\lambda }_1$
• D. Cannot be predicted

Answer 1

The correct option is C ${\lambda }_2<{\lambda }_1$

As reflected wave is inverted in shape as compared to the incident wave, therefore, wave is travelling from rarer medium to comparatively denser medium.

So, $v_2<v_1,v_2$ is velocity of transmitted wave and $v_1$ is velocity of incident wave.
Also, we know frequency $f$ will remain same in both medium.
$\therefore \frac{v_1}{{\lambda }_1}=\frac{v_2}{{\lambda }_2}=f$, where ${\lambda }_1$ is wavelength of incident wave and ${\lambda }_2$ is wavelength of transmitted wave.
$\Rightarrow \frac{v_1}{v_2}=\frac{{\lambda }_1}{{\lambda }_2}$
$\Rightarrow {\lambda }_1>{\lambda }_2$ [ $\because v_1>v_2$ ]