Intro to Standing Waves

Q. 24.19. The equation of a simple harmonic wave is given byy 3in (50t x), where x and y are in metresand t is in seconds. The ratio of maximum particle2velocity to the wave velocity isAIPMT (Mains)-2012\rbrack3223(1)225.(3)320. A train moving at a speed of 220 ms1 towards a

Q.

At a certain instant a stationary transverse wave is found to have maximum kinetic energy. The appearance of string at that instant is

1. Sinusoidal shape with amplitude A/2

2. Sinusoidal shape with amplitude A

3. Sinusoidal shape with amplitude A/3

4. Straight line

Q. Stationary waves are formed due to superposition of

1. two identical waves travelling in same directions.
2. two identical waves travelling in opposite directions.
3. two unlike waves travelling in same directions.
4. two unlike waves travelling in opposite directions.

Q.

Equation of longitudinal stationary waves in the pipe is

1. 

2. 

3. 

4. 

Q. Standing wave is produced in $10\text{m}$ long stretched string. If the string vibrates in $5$ segments and wave velocity is $20\text{m/s}$, then frequency of oscillation is

1. $5\text{Hz}$
2. $2\text{Hz}$
3. $8\text{Hz}$
4. $7\text{Hz}$

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

1. False
2. True

Q. In a stationary wave, when particles of a string passes through their mean position then kinetic energy of these particles at antinodes is

1. Minimum
2. Maximum
3. Zero
4. Infinite

Q.

Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is 1 : 4 : 9 : 16 then the ratio of their fundamental frequencies are

[KCET 2000]

1. 16 : 9 : 4 : 1

2. 4 : 3 : 2 : 1

3. 1 : 4 : 2 : 16

4. 1 : 2 : 3 : 4

Q. A thin wire of length $99\text{cm}$ is fixed at both ends. The wire has some tension and is divided into three segments of lengths $l_1,l_2$, and $l_3$ as shown in the figure. If these segments are made to vibrate, with their fundamental frequencies respectively in the ratio $1:2:3$, then the lengths $l_1,l_2,l_3$ respectively are (in $\text{cm}$):

1. $27,54,18$
2. $18,27,54$
3. $54,27,18$
4. $27,9,18$

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

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

Q. A steel wire of length $1\text{m}$ and mass $0.1\text{kg}$, having a uniform cross-sectional area of ${10}^{-6}{\text{m}}^2$ is rigidly fixed at both ends. The temperature of the wire is lowered by ${20}^{\circ }\text{C}$. If the wire is vibrating in harmonic motion, pick from the following possible frequencies of motion (in $\text{Hz}$)
Given Young's modulus of steel $Y=2\times {10}^{11}{\text{N/m}}^2,\alpha =1.21\times {10}^{-5}/{}^{\circ }\text{C}$

1. 11
2. 22
3. 10
4. 20

Q. Two travelling waves $y_1=\text{A sin [k(x - ct)]}$ and $y_2=\text{A sin}\left[k\right(x+ct\left)\right]$ are superimposed on string. The distance between adjacent nodes is

1. $\frac{c}{\pi }$
2. $\frac{c}{2\pi }$
3. $\frac{\pi }{2k}$
4. $\frac{\pi }{k}$

Q. A standing wave is produced on a string clamped at one end and free at the other. The length of the string
(a) must be an integral multiple of $\lambda /4$
(b) must be an integral multiple of $\lambda /2$
(c) must be an integral multiple of $\lambda$
(d) must be an integral multiple of $\lambda /2$.