The equation of stationary wave along a stretched string is given… - Vidyadip

MCQ

The equation of stationary wave along a stretched string is given by $y = 5\sin \frac{{\pi x}}{3}\cos 40\pi t$ where $x$ and $y$ are in centimetre and $t$ in second. The separation between two adjacent nodes is .... $cm$

A
$6$
B
$4$
✓
$3$
D
$1.5$

✓

Answer

Correct option: C.

$3$

c
(c) Given $y = 5\sin \frac{{\pi x}}{3}\cos 40\,\pi t$

Comparing with $y = 2a\cos \frac{{2\pi vt}}{\lambda }\sin \frac{{2\pi x}}{\lambda }$$ \Rightarrow \lambda = 6\,cm.$

$\therefore$ The separation between adjacent nodes $ = \frac{\lambda }{2} = 3\,cm.$

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