Q. No.A transverse wave on a string is described by \(y=3 \sin (36 t+0.018 x+\pi / 4) .\) where \( x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is: (in cm) (Nearest integer)
1. \(300\)
2. \(200\)
3. \(349\)
4. \(450\)
1. \(300\)
2. \(200\)
3. \(349\)
4. \(450\)
Subtopic: Â Wave Motion |
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Displacement of a wave is expressed as \(x(t) = 5\cos(628t+\pi/2)~\text m. \) The wavelength of the wave when its velocity is \(300 ~\text{m/s} \) is: \((\pi=3.14 )\)
1. \(5~\text m\)
2. \(0.5~\text m\)
3. \(3~\text m\)
4. \(0.33~\text m\)
1. \(5~\text m\)
2. \(0.5~\text m\)
3. \(3~\text m\)
4. \(0.33~\text m\)
Subtopic: Â Wave Motion |
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A sinusoidal wave of wavelength \(7.5 ~\text{cm}\) travels a distance of \(1.2 ~\text{cm}\) along the \(x\text-\)direction in \(0.3 \text{ sec.}\) The crest \(P\) is at \(x=0 \) at \(t=0 \) sec and maximum displacement of the wave is \(2 ~\text{cm.}\) Which equation correctly represents this wave?
1. \(y=2 \cos (0.13 x-0.50 t)~ \text{cm}\)
2. \(y=2 \cos (0.83 x-3.35 t) ~\text{cm}\)
3. \(y=2 \sin (0.83 x-3.50 t) ~\text{cm}\)
4. \(y=2 \cos (3.35 x-0.83 t)~ \text{cm}\)
1. \(y=2 \cos (0.13 x-0.50 t)~ \text{cm}\)
2. \(y=2 \cos (0.83 x-3.35 t) ~\text{cm}\)
3. \(y=2 \sin (0.83 x-3.50 t) ~\text{cm}\)
4. \(y=2 \cos (3.35 x-0.83 t)~ \text{cm}\)
Subtopic: Â 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
1. \(2\) m/s
2. \(4\) m/s
3. \(0.5\) m/s
4. \(0.25\) m/s
Subtopic: Â 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
1. \(1/2\)
2. \(1\)
3. \(2\)
4. none of these
Subtopic: Â 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. \(50\)
1. \(32\)
2. \(23\)
3. \(16\)
4. \(50\)
Subtopic: Â 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: Â 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. \(400 \sqrt 2~\text{m/s}\)
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: Â 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. \(2\)
1. \( 4 \pi\)
2. \( 2 \pi\)
3. \(\pi\)
4. \(2\)
Subtopic: Â Wave Motion |
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At time \(t=0,\) the displacement of a wave moving in the positive \(x\text-\)direction is given by; \(y=\dfrac{1}{1+(x)^2},\) and at \(t=1~\text{s},\) it becomes \(y=\dfrac{1}{1+(x-2)^2},\) where \(x\) and \(y\) are in meters. Assuming the wave maintains its shape during propagation, what is the velocity of the wave?
| 1. | \(6~\text{m/s}\) | 2. | \(4~\text{m/s}\) |
| 3. | \(8~\text{m/s}\) | 4. | \(2~\text{m/s}\) |
Subtopic: Â Wave Motion |
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