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Question

A transverse wave of amplitude $$0.5$$ m and wavelength $$1$$ m and frequency $$2$$ Hz is propagating in a string in the negative x direction. The expression for this wave is?


A
y=0.5sin(πx2πt)
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B
y=0.5sin(2πx4πt)
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C
y=0.5sin(2πx+4πt)
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D
y=0.5sin(2πx+2πt)
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Solution

The correct option is D $$y=0.5\sin(2\pi x+4\pi t)$$
Equation of a transverse wave propagating in the negative x direction can be written as    $$y= A \ \sin (kx+wt)$$
Now,  amplitude   $$A = 0.5 \ m$$
Given :   $$\lambda = 1 \ m$$              $$\nu = 2 \ Hz$$
So,   $$w = 2\pi \nu = 2\pi \times 2 = 4\pi$$
Also,  $$k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{1} = 2\pi$$
So,    $$y = 0.5  \ \sin(2\pi x + 4\pi t)$$
Option C is correct.

Physics

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