JEE MAIN - Physics (2021 - 17th March Evening Shift - No. 1)
A sound wave of frequency 245 Hz travels with the speed of 300 ms$$-$$1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?
Y(x, t) = 0.03 [ sin 5.1x $$-$$ (0.2 $$\times$$ 103)t ]
Y(x, t) = 0.03 [ sin 5.1x $$-$$ (1.5 $$\times$$ 103)t ]
Y(x, t) = 0.06 [ sin 5.1x $$-$$ (1.5 $$\times$$ 103)t ]
Y(x, t) = 0.06 [ sin 0.8x $$-$$ (0.5 $$\times$$ 103)t ]
Explanation
$$Y = A\sin (kx - \omega t)$$
$$A = {6 \over 2}$$ = 3cm = 0.03 m
$$\omega = 2\pi f = 2\pi \times 245$$
$$\omega = 1.5 \times {10^3}$$
$$k = {\omega \over v} = {{1.5 \times {{10}^3}} \over {300}}$$
$$k = 5.1$$
$$y = 0.03\sin (5.1x - (1.5 \times {10^3})t)$$
$$A = {6 \over 2}$$ = 3cm = 0.03 m
$$\omega = 2\pi f = 2\pi \times 245$$
$$\omega = 1.5 \times {10^3}$$
$$k = {\omega \over v} = {{1.5 \times {{10}^3}} \over {300}}$$
$$k = 5.1$$
$$y = 0.03\sin (5.1x - (1.5 \times {10^3})t)$$
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