The equation of a stationary wave along a str | vedclass

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(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 = 2a \sin(k

Vedclass · Accepted Answer

$1.5$

Vedclass · Answer

(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 $y = 2a \sin(kx) \cos(\omega t)$. Comparing the given equation with the standard form,we get the wave number $k = \frac{2\pi}{3}$. Since $k = \frac{2\pi}{\lambda}$,we have $\frac{2\pi}{\lambda} = \frac{2\pi}{3}$,which gives the wavelength $\lambda = 3 \, cm$. The separation between two adjacent nodes in a stationary wave is given by $\frac{\lambda}{2}$. Therefore,the separation is $\frac{3}{2} = 1.5 \, cm$.

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 ..... $cm$.

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