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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Which one of the following does not represent a traveling wave :

(1) $y=\mathrm{sin}\left(x-v\text{\hspace{0.17em}}t\right)$

(2) $y={y}_{m}\mathrm{sin}k\left(x+v\text{\hspace{0.17em}}t\right)$

(3) $y={y}_{m}\mathrm{sin}\left(x-v\text{\hspace{0.17em}}t\right)$

(4) $y=f\left({x}^{2}-v\text{\hspace{0.17em}}{t}^{2}\right)$

Concept Questions :-

Wave motion
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Wave equations of two particles are given by ${y}_{1}=a\mathrm{sin}\left(\omega \text{\hspace{0.17em}}t-kx\right)$, ${y}_{2}=a\mathrm{sin}\left(kx+\omega \text{\hspace{0.17em}}t\right)$, then :

(1) They are moving in the opposite direction

(2) The phase between them is 90°

(3) The phase between them is 180°

(4) The phase between them is 0°

Concept Questions :-

Wave motion
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A transverse wave is represented by the equation $y={y}_{0}\mathrm{sin}\frac{2\pi }{\lambda }\left(vt-x\right)$

For what value of λ, the maximum particle velocity equal to two times the wave velocity?

(1) $\lambda =2\pi {y}_{0}$

(2) $\lambda =\pi {y}_{0}/3$

(3) $\lambda =\pi {y}_{0}/2$

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

Concept Questions :-

Wave motion
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A wave travels in a medium according to the equation of displacement given by $y\left(x,\text{\hspace{0.17em}}t\right)=0.03\mathrm{sin}\pi \left(2t-0.01x\right)$ where y and x are in metres and t in seconds. The wavelength of the wave is :

(1) 200 m

(2) 100 m

(3) 20 m

(4) 10 m

Concept Questions :-

Wave motion
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Equation of a progressive wave is given by $y=4\mathrm{sin}\left\{\pi \left(\frac{t}{5}-\frac{x}{9}\right)+\frac{\pi }{6}\right\}$

Then which of the following is correct ?

(1) v = 5 m / sec

(2) λ = 18 m

(3) a = 0.04 m

(4) n = 50 Hz

Concept Questions :-

Wave motion
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