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

MCQ

The equation of a stationary wave along a stretched string is given by $y = 5\,sin\, \frac{2\pi }{3}x\, cos\, 40\pi t$ where $x$ and $y$ are in $cm$ and $t$ is in $s$. The separation between two adjacent nodes is ..... $cm$

✓
$1.5$
B
$3$
C
$6$
D
$4$

✓

Answer

Correct option: A.

$1.5$

a
The given equation of a stationary wave is $y$

$=5 \sin \frac{2 \pi}{3} x \cos 40 \pi t$

The standard equation of a stationary wave is

$y=2 a \sin k x \cos \omega t$

Comparing $(i)$ and $(ii),$ we get $\mathrm{k}=\frac{2 \pi}{3}$

or $\frac{2 \pi}{\lambda}=\frac{2 \pi}{3}$ or $\lambda=3 \mathrm{\,cm}$

Separation between two adjacent nodes is

$\frac{\lambda}{2}=\frac{3}{2}=1.5 \mathrm{\,cm}$

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