A wave in a string has an amplitude of 2, cm. | vedclass

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Question

(A) Given: Amplitude $A = 2\, cm = 0.02\, m$,speed $v = 128\, m/s$.Since $5$ complete waves fit in $4\, m$,the wavelength $\lambda = \frac{4\, m}{5} =

Vedclass · Accepted Answer

$y = 0.02\, m\, \sin(7.85x - 1005t)$

Vedclass · Answer

(A) Given: Amplitude $A = 2\, cm = 0.02\, m$,speed $v = 128\, m/s$.Since $5$ complete waves fit in $4\, m$,the wavelength $\lambda = \frac{4\, m}{5} = 0.8\, m$.The frequency $f = \frac{v}{\lambda} = \frac{128}{0.8} = 160\, Hz$.The angular frequency $\omega = 2\pi f = 2 	imes 3.14159 	imes 160 \approx 1005\, rad/s$.The wave number $k = \frac{2\pi}{\lambda} = \frac{2 	imes 3.14159}{0.8} \approx 7.85\, rad/m$.Since the wave travels in the $+ve$ $x$-direction,the equation is $y = A \sin(kx - \omega t)$.Substituting the values: $y = 0.02 \sin(7.85x - 1005t)$.

$A$ wave in a string has an amplitude of $2\, cm$. The wave travels in the $+ve$ direction of $x-$axis with a speed of $128\, m/s$ and it is noted that $5$ complete waves fit in $4\, m$ length of the string. The equation describing the wave is

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