A wave traveling in the +ve $$x$$-direction having maximum displacement along $$y$$-direction as $$1~\text{m}$$, wavelength $$2\pi ~\text{m}$$ and frequency of $$\frac{1}{\pi}~\text{Hz}$$, is represented by:
1. $$y=\sin (2 \pi x-2 \pi t)$$
2. $$y=\sin (10 \pi x-20 \pi t)$$
3. $$y=\sin (2 \pi x+2 \pi t)$$
4. $$y=\sin (x-2 t)$$

Subtopic:  Wave Motion |
86%
From NCERT
AIPMT - 2013
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The equation of a simple harmonic wave is given by $$y=3\sin \frac{\pi}{2}(50t-x)$$ where $$x$$ and $$y$$ are in meters and $$t$$ is in seconds. The ratio of maximum particle velocity to the wave velocity is:
1. $$\frac{3\pi}{2}$$
2. $$3\pi$$
3. $$\frac{2\pi}{3}$$
4. $$2\pi$$

Subtopic:  Wave Motion |
74%
From NCERT
AIPMT - 2012
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Two waves are represented by the equations ${y}_{1}=a$ $\mathrm{sin}\left(\omega t+kx+0.57\right)$ $m$ and
${y}_{2}=a\mathrm{cos}\left(\omega t+kx\right)$ $m$, where $$x$$ is in metres and $$t$$ in seconds. The phase difference between them is:
1. $$1.25$$ rad
2. $$1.57$$ rad
3. $$0.57$$ rad
4. $$1.0$$ rad

Subtopic:  Wave Motion |
67%
From NCERT
AIPMT - 2011
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A transverse wave is represented by y = Asin(ωt -kx). At what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. $\pi$A/2

2. $\pi$A

3. 2$\pi$A

4. A

Subtopic:  Wave Motion |
84%
From NCERT
AIPMT - 2010
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A wave in a string has an amplitude of 2 cm. The wave travels in the positive direction of the x-axis with a speed of 128 m/s and it is noted that 5 complete waves fit in the 4 m length of the string. The equation describing the wave is:

 1 y = (0.02)m sin(7.85x+1005t) 2 y = (0.02)m sin(15.7x -2010t) 3 y = (0.02)m sin(15.7x+2010t) 4 y = (0.02)m sin(7.85x -1005t)

Subtopic:  Wave Motion |
72%
From NCERT
AIPMT - 2009
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The wave described by $$y=0.25\sin (10\pi x-2\pi t)$$, where $$x$$ and $$y$$ are in metre and $$t$$ in second, is a wave travelling along the:

 1 –ve x-direction with frequency $$1$$ Hz 2 +ve x-direction with frequency $$\pi$$ Hz and wavelength  $$\lambda=0.2$$ m 3 +ve x-direction with frequency $$1$$ Hz and wavelength  $$\lambda=0.2$$ m 4 –ve x-direction with amplitude $$0.25$$ m and wavelength  $$\lambda=0.2$$ m

Subtopic:  Wave Motion |
84%
From NCERT
AIPMT - 2008
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A transverse wave propagating along the x-axis is represented by:
$$y=(x,t)=8.0\mathrm{sin}(0.5\pi x-4\pi t-\frac{\pi}{4})$$ where $$x$$ is in meters and $$t$$ in seconds. The speed of the wave is:
1. $$4\pi$$ m/s
2. $$0.5$$ m/s
3. $$\frac{\pi}{4}$$ m/s
4. $$8$$ m/s

Subtopic:  Wave Motion |
82%
From NCERT
AIPMT - 2006
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