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Question

(B) The standard equation of a transverse harmonic wave is given by $y = A \sin (\omega t + kx + \phi)$.Comparing this with the given equation $y = 3

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$3$

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(B) The standard equation of a transverse harmonic wave is given by $y = A \sin (\omega t + kx + \phi)$.Comparing this with the given equation $y = 3 \sin (36t + 0.018x + \frac{\pi}{4})$,we identify the wave number $k = 0.018 \, cm^{-1}$.The distance between two successive crests is equal to the wavelength $\lambda$.The relationship between wavelength and wave number is $\lambda = \frac{2\pi}{k}$.Substituting the value of $k$: $\lambda = \frac{2 	imes 3.1416}{0.018} \approx 349.06 \, cm$.To convert this into meters,we divide by $100$: $\lambda = \frac{349.06}{100} \approx 3.49 \, m$.Rounding to the nearest provided option,the distance is $3.5 \, m$.

$A$ transverse harmonic wave on a string is described by $y = 3 \sin (36t + 0.018x + \frac{\pi}{4})$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The least distance between two successive crests in the wave is .... $m$. (in $.5$)

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