Question 154: Waves

Question

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?

Accepted Answer

$$Y = A\sin (kx - \omega t)$$
$$A = {6 \over 2}$$ = 3cm = 0.03 m
$$\omega  = 2\pi f = 2\pi  	imes 245$$
$$\omega  = 1.5 	imes {10^3}$$
$$k = {\omega  \over v} = {{1.5 	imes {{10}^3}} \over {300}}$$
$$k = 5.1$$
$$y = 0.03\sin (5.1x - (1.5 	imes {10^3})t)$$

Answer

Y(x, t) = 0.03 [ sin 5.1x $$-$$ (0.2 $$	imes$$ 103)t ]

Answer

Y(x, t) = 0.03 [ sin 5.1x $$-$$ (1.5 $$	imes$$ 103)t ]

Answer

Y(x, t) = 0.06 [ sin 5.1x $$-$$ (1.5 $$	imes$$ 103)t ]

Answer

Y(x, t) = 0.06 [ sin 0.8x $$-$$ (0.5 $$	imes$$ 103)t ]

Waves

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?

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