The equation of a wave is $y=2\mathrm{sin}\pi \left(0.5x-200t\right)$, where x and y are expressed in cm and t in sec. The wave velocity is :

(1) 100 cm/sec

(2) 200 cm/sec

(3) 300 cm/sec

(4) 400 cm/sec

Concept Questions :-

Wave motion
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Equation of a progressive wave is given by

$y=0.2\mathrm{cos}\pi \left(0.04t+.02x-\frac{\pi }{6}\right)$

The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of π/2 :

(1) 4 cm

(2) 8 cm

(3) 25 cm

(4) 12.5 cm

Concept Questions :-

Types of waves
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Two waves are given by ${y}_{1}=a\mathrm{sin}\left(\omega t-kx\right)$ and ${y}_{2}=a\mathrm{cos}\left(\omega \text{\hspace{0.17em}}t-kx\right)$. The phase difference between the two waves is :

(1) $\frac{\pi }{4}$

(2) π

(3) $\frac{\pi }{8}$

(4) $\frac{\pi }{2}$

Concept Questions :-

Types of waves
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If the amplitude of waves at distance r from a point source is A, the amplitude at a distance 2r will be :

(1) 2A

(2) A

(3) A/2

(4) A/4

Concept Questions :-

Wave motion
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A wave is reflected from a rigid support. The change in phase on reflection will be :

(1) π/4

(2) π/2

(3) π

(4) 2π

Concept Questions :-

Wave motion
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A plane wave is represented by $x=1.2\mathrm{sin}\left(314\text{\hspace{0.17em}}t+12.56y\right)$

Where x and y are distances measured along in x and y direction in meters and t is time in seconds. This wave has

(1) A wavelength of 0.25 m and travels in + ve x-direction

(2) A wavelength of 0.25 m and travels in + ve y-direction

(3) A wavelength of 0.5 m and travels in – ve y-direction

(4) A wavelength of 0.5 m and travels in – ve x-direction

Concept Questions :-

Types of waves
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The equation of a wave traveling in a string can be written as $y=3\mathrm{cos}\pi \left(100\text{\hspace{0.17em}}t-x\right)$. Its wavelength is :

(1) 100 cm

(2) 2 cm

(3) 5 cm

(4) None of the above

Concept Questions :-

Types of waves
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A transverse wave is described by the equation $y={Y}_{0}\mathrm{sin}\left(2\mathrm{\pi ft}-\frac{2\mathrm{\pi }}{\mathrm{\lambda }}\mathrm{x}\right)$. The maximum particle velocity is four times the wave velocity if :

(1) $\lambda =\frac{\pi {Y}_{0}}{4}$

(2) $\lambda =\frac{\pi {Y}_{0}}{2}$

(3) $\lambda =\pi {Y}_{0}$

(4) $\lambda =2\pi {Y}_{0}$

Concept Questions :-

Types of waves
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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 :

(1) $y\left(x,\text{\hspace{0.17em}}t\right)=0.5\mathrm{sin}\left(2\pi x-4\pi t\right)$

(2) $y\left(x,\text{\hspace{0.17em}}t\right)=0.5\mathrm{cos}\left(2\pi x+4\pi t\right)$

(3) $y\left(x,\text{\hspace{0.17em}}t\right)=0.5\mathrm{sin}\left(\pi x-2\pi t\right)$

(4) $y\left(x,\text{\hspace{0.17em}}t\right)=0.5\mathrm{cos}\left(2\pi x+2\pi t\right)$

Concept Questions :-

Types of waves
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The displacement of a particle is given by $y=5×{10}^{-4}\mathrm{sin}\left(100t-50x\right)$, where x is in meter and t is in  sec, find out the velocity of the wave :

(1) 5000 m/sec

(2) 2 m/sec

(3) 0.5 m/sec

(4) 300 m/sec

Concept Questions :-

Wave motion
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