PrepBharat

1.A plane wave is represented by
\[x=1.2\sin \left(314 t + 12.56 y\right)\]
Where x and y are distances measured along in x and y direction in meters and t is time in seconds. This wave has
a) A wavelength of 0.25 m and travels in + ve x direction
b) A wavelength of 0.25 m and travels in + ve y direction
c) A wavelength of 0.5 m and travels in – ve y direction
d) A wavelength of 0.5 m and travels in – ve x direction

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2.The equation of a wave travelling in a string can be written as \[y=3 \cos \pi \left(100 t - x\right)\]     . Its wavelength is
a)100 cm
b) 2 cm
c) 5 cm
d) None of the above

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3.A transverse wave is described by the equation \[Y=Y_{0} \sin 2\pi \left(ft - \frac{x}{\lambda}\right)\]     . The maximum particle velocity is four times the wave velocity if
a) \[\lambda =\frac{\pi Y_{0}}{4}\]
b) \[\lambda =\frac{\pi Y_{0}}{2}\]
c) \[\lambda =\pi Y_{0}\]
d) \[\lambda = 2\pi Y_{0}\]

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4. A wave equation which gives the displacement along the Y direction is given by the equation \[Y=10^{4} \sin \left(60 t + 2x\right)\]     , where x and y are in metres and t is time in seconds. This represents a wave
a) Travelling with a velocity of 30 m/sec in the negative X direction
b) Of wavelength \[\pi\]  metre
c) Of frequency \[30/\pi\]  Hz
d) All of the Above

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5.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) \[y(x, t) = 0.5 \sin\left(2\pi x- 4 \pi t\right)\]
b) \[y(x, t) = 0.5 \cos\left(2\pi x+ 4 \pi t\right)\]
c) \[y(x, t) = 0.5 \sin\left(\pi x- 2 \pi t\right)\]
d) \[y(x, t) = 0.5 \cos\left(2\pi x+ 2 \pi t\right)\]

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6. The displacement of a particle is given by \[y = 5\times 10^{-4}\sin \left(100t-50 x\right)\]      , where x is in meter and t in sec, find out the velocity of the wave
a) 5000 m/sec
b) 2 m/sec
c) 0.5 m/sec
d) 300 m/sec

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7. Which one of the following does not represent a travelling wave
a) \[y = \sin \left(x-v t\right)\]
b) \[y =y_{m} \sin K \left(x-v t\right)\]
c) \[y =y_{m} \sin log \left(x-v t\right)\]
d) y = f (x² - v t²)

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8.A wave represented by the given equation \[y =A\sin \left(10 \pi x+ 15 \pi t+\frac{\pi}{3}\right)\]      , where x is in meter and t is in second. The expression represents
a) A wave travelling in the positive X direction with a velocity of 1.5 m/sec
b) A wave travelling in the negative X direction with a velocity of 1.5 m/sec
c) A wave travelling in the negative X direction with a wavelength of 0.2 m
d) Both b and c

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9.A plane wave is described by the equation \[y =3\cos \left(\frac{x}{4}-10 t-\frac{\pi}{2}\right)\]     . The maximum velocity of the particles of the medium due to this wave is
a) 30
b) \[\frac{3\pi}{2}\]
c) 3/4
d) 40

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10.The path difference between the two waves
\[y_{1} =a_{1} \sin \left(\omega t -\frac{2\pi x}{\lambda}\right)\]     and \[y_{2} =a_{2} \cos \left(\omega t -\frac{2\pi x}{\lambda}+\phi\right)\]      is
a) \[\frac{\lambda}{2\pi}\phi\]
b) \[\frac{\lambda}{2\pi}\left(\phi+\frac{\pi}{2}\right)\]
c) \[\frac{2\pi}{\lambda}\left(\phi-\frac{\pi}{2}\right)\]
d) \[\frac{2\pi}{\lambda}\phi\]

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