A progressive wave travelling along the positive \(x\)-direction is represented by \(y(x,t)=A\sin(kx-\omega t+\phi)\). Its snapshot at \(t=0\) is given in the figure.

         
For this wave, the phase \(\phi\) is:
1. \(\frac{\pi}{2}\)
2. \(\pi\)
3. \(0\)
4. \(-\frac{\pi}{2}\)

Subtopic:  Wave Motion |
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For a transverse wave travelling along a straight line, the distance between two peaks (crests) is \(5~\text{m}\), while the distance between one crest and one trough is \(1.5~\text{m}\). The possible wavelengths (in m) of the waves are:
1. \(1,2,3, \dots\)
2. \(\frac{1}{1},\frac{1}{3},\frac{1}{5},\dots\)
3. \(\frac{1}{2},\frac{1}{4},\frac{1}{6},\dots\)
4. \(1,3,5, \dots\)

Subtopic:  Wave Motion |
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Which, of the following equation represents a travelling wave?
1. \(y=A\sin(15x-2t)\)
2. \(y=Ae^{-x^2}(vt+\theta)\)
3. \(y=Ae^{x}\cos (\omega t-\theta)\)
4. \(y=A\sin x \cos \omega t\)

Subtopic:  Wave Motion |
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A longitudinal wave is represented by \(x = 10 ~\sin ~2 \pi \left( nt- {\dfrac x \lambda}\right)\) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:
1. \(2 \pi\) cm 2. \(5 \pi\) cm
3. \(\pi\) cm 4. \({\dfrac {5 \pi} 2}\) cm
Subtopic:  Wave Motion |
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A transverse wave is represented by \(y = 2 \sin ( \omega t - kx) ~\text{cm}.\) The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be:
1. \( 4 \pi\)
2. \( 2 \pi\)
3. \(\pi\)
4. \(2\)
Subtopic:  Wave Motion |
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In the wave equation, \({y}=0.5 \sin \dfrac{2 \pi}{\lambda}(400 {t}-{x}) ~{\text m}, \) the velocity of the wave will be: 
1. \(200~\text{m/s}\)
2. \(200 \sqrt 2~\text{m/s}\)
3. \(400~\text{m/s}\)
4. \(400 \sqrt 2~\text{m/s}\)
Subtopic:  Wave Motion |
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The equation of wave is given as \(y=0.05 \sin(2x-4t),\) where \(x \) in meters and \(t\) in seconds. The velocity of the wave is equal to:
1. \(2\) m/s
2. \(4\) m/s
3. \(0.5\) m/s
4. \(0.25\) m/s
Subtopic:  Wave Motion |
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If the angular frequency of the given motion \(y = sin ( \omega t) + cos (\omega t)\) is \(k \omega\), then value of \(k\) is: 
1. \(1/2\)
2. \(1\)
3. \(2\)
4. none of these
Subtopic:  Wave Motion |
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The equation of a progressive wave is given by;   \(y = A \text{sin} (160t - 0.5x),\) where \(x\) and \(y\) are in metres and \(t\) is in seconds. If the speed of the wave is \(10 x\) m/s, then \(x=\)
1. \(32\)
2. \(23\)
3. \(16\)
4. \(50\)
Subtopic:  Wave Motion |
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