Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
A wave is represented by the equation \[y=A\sin (10\pi x+15\pi t+\pi /3)\] where\[x\]is in metres and t is in seconds. The expression represents: a wave travelling in the positive \[x-\]direction with a velocity 1.5 m/s (2) a wave travelling in the negative \[x-\]direction with a velocity 1.5 m/s (3) a wave travelling in the negative \[x-\]direction with a wavelength 0.2 m (4) a wave travelling in the positive \[x-\]direction with a wavelength 0.2 mA) 1 and 2 are correct
B) 2 and 3 are correct
C) 1 and 4 are correct
D) 1, 2 and 3 are correct
Correct Answer: B
Solution :
From the equation of wave \[\omega =15\pi ,k=10\pi \] Speed of wave, \[v=\frac{\omega }{k}=\frac{15\pi }{10\pi }=1.5m/s\] Wavelength of wave, \[\lambda =\frac{2\pi }{k}-=\frac{2\pi }{10\pi }=0.2m\] In the equation\[10\pi x\]and\[15\pi t\]have the same sign. Therefore, wave is travelling in negative \[x-\]direction.
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