Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A wave in a string has an amplitude of $2 \text{ cm}$ . The wave travels in the +ve direction of x-axis with a speed of $128 \text{ ms}^{-1}$ and it is noted that $5$ complete waves fit in $4 \text{ m}$ length of the string. The equation describing the wave is:

$y=(0.02)\text{ m} \sin(7.85x+1005t)$

$y=(0.02)\text{ m} \sin(15.7x-2010t)$

$y=(0.02)\text{ m} \sin(15.7x+2010t)$

$y=(0.02)\text{ m} \sin(7.85x-1005t)$

Step-by-Step Solution

Determine the Amplitude ( $A$ ): The amplitude is given as $2 \text{ cm} = 0.02 \text{ m}$ .
Calculate the Wavelength ( $\lambda$ ): It is given that $5$ complete waves fit in a length of $4 \text{ m}$ . Therefore, $5\lambda = 4 \text{ m} \implies \lambda = \frac{4}{5} = 0.8 \text{ m}$ .
Calculate the Wave Number ( $k$ ): The wave number is $k = \frac{2\pi}{\lambda}$ . $k = \frac{2\pi}{0.8} = 2.5\pi \approx 2.5 \times 3.14 = 7.85 \text{ rad/m}$
Calculate the Angular Frequency ( $\omega$ ): The wave speed is $v = \frac{\omega}{k}$ , so $\omega = v \cdot k$ . $\omega = 128 \times 7.85 = 1004.8 \approx 1005 \text{ rad/s}$
Determine the Wave Equation: The general equation for a wave travelling in the positive x-direction is $y = A\sin(kx - \omega t)$ or $y = A\sin(\omega t - kx)$ . Looking at the options, we use the form $y = A\sin(kx - \omega t)$ . Substituting the values, we get: $y = 0.02 \sin(7.85x - 1005t)$

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