A composition string is made up by joining two strings of differe… - Vidyadip

MCQ

A composition string is made up by joining two strings of different masses per unit length $\rightarrow \mu$ and $4\mu$ . The composite string is under the same tension. A transverse wave pulse $: Y = (6 mm) \,\,sin\,\,(5t + 40x),$ where $‘t’$ is in seconds and $‘x’$ in meters, is sent along the lighter string towards the joint. The joint is at $x = 0$. The equation of the wave pulse reflected from the joint is

A
$(2 mm) \,\, sin\,\,(5t - 40x)$
B
$(4 mm) \,\,sin\,\,(40x - 5t)$
✓
$- (2 mm) \,\,sin\,\,(5t - 40x)$
D
$(2 mm)\,\, sin \,\,(5t - 10x)$

✓

Answer

Correct option: C.

$- (2 mm) \,\,sin\,\,(5t - 40x)$

c
$V_{1}=\sqrt{\frac{T}{\mu}}, V_{2}=\sqrt{\frac{T}{4 \mu}} V_{2} \leq V_{1}$

$\Rightarrow 2^{n d}$ isdanser $\Rightarrow$ phasechan $\geq$ of $\pi$

wave reflected from denser medium

$\Rightarrow A_{r}=\frac{V_{2}-V_{1}}{V_{2}}+V_{1} \times 6=\frac{\frac{v_{1}}{2}-V_{1}}{\frac{V_{2}}{2}+V_{1}} \times 6=-2 \mathrm{mm}$

$e q^{n} \Rightarrow-(2 m m) \sin (5 t-40 x)$

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