Intro to Standing Waves

Q. Statement I : In a standing wave the energy is confined between the two nodes.
Statement II : In a standing wave all the particles between two nodes have different amplitudes.

1. Both the statements are correct but statement II doesnt explain statement I.
2. Statement I is correct but statement II is incorrect.
3. Statement I is incorrect but statement II is correct.
4. Both the statements are correct and statement II correctly explains statement I.

Q. The points where displacement is zero are called nodes and the points where the displacement is maximum are called antinodes.

1. True
2. False

Q. In stationary waves, energy is uniformly distributed.

1. False
2. True

Q. In a standing wave, the energy is confined between two nodes.

1. False
2. True

Q. In a standing wave, all the particles between two consecutive node and antinode have different amplitudes.

1. False
2. True

Q. Standing waves are formed when two waves of equal wavelength and equal amplitude travel along the same path with equal speeds in opposite directions.

1. False
2. True

Q. Consider the three waves, $z_1,z_2$ and $z_3$ as $z_1=\text{A sin}(kx-\omega t),z_2=\text{A sin}(kx+\omega t)$ and $z_3=\text{A sin}(ky-\omega t)$. Which of the following represents a standing wave?

1. $z_1+z_2$
2. $z_2+z_3$
3. $z_3+z_1$
4. $z_2+2z_3$

Q. When a stationary wave is formed, its frequency is

1. Same as that of the individual waves
2. Thrice as that of the individual waves
3. Twice as that of the individual waves
4. Half as that of the individual waves

Q. Stationary waves of frequency $300\text{Hz}$ are formed in a string, in which the velocity of wave is $200\text{m/s}$. The distance between a node and the consecutive antinode is

1. $\frac{1}{6}\text{m}$
2. $2\text{m}$
3. $\frac{3}{2}\text{m}$
4. $4\text{m}$

Q. A wave represented by the equation $y=a\cos (\omega t-kx)$ is superimposed with another wave to form a stationary wave such that the point $x=0$ is a node. The equation of the other wave is

1. $a\cos (\omega t-kx)$
2. $-a\cos (\omega t+kx)$
3. $a\sin (\omega t-kx)$
4. $-a\sin (\omega t-kx)$