Intuition of Wave Speed

Q. The displacement of a particle of a string carrying a travelling wave is given by $y=3\sin \left[6.28\right(0.50x-50t\left)\right]$
$(x\to \text{in cm},y\to \text{cm},t\to \text{in second})$.
What would be the speed of the wave?

1. $200{\text{cm s}}^{-1}$
2. $150{\text{cm s}}^{-1}$
3. $100{\text{cm s}}^{-1}$
4. $50{\text{cm s}}^{-1}$

Q. For a plane progressive wave represented by, $y=5\sin (100\pi t-0.4\pi x)$, what is the wave velocity (in $\text{m/s}$)?

1. $350$
2. $250$
3. $200$
4. $180$

Q. For a plane progressive wave represented by, $y=5\sin (100\pi t-0.4\pi x)$, what is the wave velocity (in $\text{m/s}$)?

1. $350$
2. $250$
3. $200$
4. $180$

Q.

The equation of a travelling wave is y = 60 cos (1800t – 6x) where y is in microns, t in seconds and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is

1. $3.6$

2. $3.6\times {10}^{-5}$

3. $3.6\times {10}^{-11}$

4. $3.6\times {10}^{-4}$

Q. The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$ here $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is

1. $300\text{m/s}$
2. $30\text{m/s}$
3. $400\text{m/s}$
4. $40\text{m/s}$

Q. The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$ here $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is

1. $300\text{m/s}$
2. $30\text{m/s}$
3. $400\text{m/s}$
4. $40\text{m/s}$

Q. The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$, where $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is (in $\text{m/s}$)

Q.

The equation of a travelling wave is y = 60 cos (1800t – 6x) where y is in microns, t in seconds and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is

1. $3.6$

2. $3.6\times {10}^{-5}$

3. $3.6\times {10}^{-11}$

4. $3.6\times {10}^{-4}$

Q. Assertion: In the equation, $y=A\sin (kx-\omega t)$ , particle starts from its mean position $x=0$ and moves towards negative $y-$axis.
Reason: The wave corresponding to given equation is travelling towards positive $x-$direction.

1. Both assertion and reason are correct and reason is the correct explanation of assertion.
2. Both assertion and reason are correct but reason is not a correct explanation of assertion.
3. Assertion is correct but reason is incorrect.
4. Assertion is incorrect but reason is correct.