Standing Wave Visualization

Q. A stretched string is vibrating according to the equation $y=5\sin \left(\frac{\pi x}{2}\right)\cos 4\pi t$, where $y$ and $x$ are in $\text{cm}$ and $t$ is in $\text{sec}$. The distance between two consecutive nodes on the string is

1. $2\text{cm}$
2. $16\text{cm}$
3. $4\text{cm}$
4. $8\text{cm}$

Q.

What is out of phase in physics?

Q.

A wave is described by the equation $y=\left(1.0mm\right)sin\pi (\frac{x}{2.0cm}-\frac{t}{0.01s})$
(a) Find the time period and the wavelength ? (b) Write the equation for the velocity of the particles. Find the speed of the particle at x = 1.0 cm at time t = 0.01 s. (c) What are the speeds of the particles at x = 3.0 cm, 5.0 cm and 7.0 cm at t = 0.01 s ? (d) What are the speeds of the particles at x = 1.0 cm at t = 0.011, 0.012, and 0.013 s?

Q.

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

1. $y=a\sin \left(kx+\omega t\right)$

2. $y=-a\cos \left(kx-\omega t\right)$

3. $y=-a\cos \left(kx+\omega t\right)$

4. $y=-a\sin \left(kx-\omega t\right)$

Q. Match the statements in column-I with the statements in column-II:

	Column-I		Column-II
(A)	A tight string is	(P)	At the middle, antinode is formed fixed at both ends in odd harmonic and sustaining standing wave
(B)	A tight string is	(Q)	At the middle, node fixed at one end is formed in even and free at ond harmonic and free at the other end
(C)	Standing wave is	(R)	At the middle, neither formed in an open node nor antinode is organ pipe. End correction formed is not negligible
(D)	Standing wave is	(S)	Phase difference formed in a closed between SHMs of organ pipe. End any two particles correction is not will be either or negligible zero.

Which of the following option has the correct combination considering column-I and Column-II.

1. B → P, R
2. D → R, S
3. C → P, Q
4. A → Q, R

Q. A particle moves with simple harmonic motion in a straight line. In first $\tau \text{s}$, after starting from rest it travels a distance $a$, and in next $\tau \text{s}$ it travels $2a$, in same direction, then :

1. Amplitude of motion is $4a$
2. Time period of oscillations is $6\tau$
3. Amplitude of motion is $3a$
4. Time period of oscillations is $8\tau$

Q. A string of length $L$ is carrying a standing wave of amplitude $A$. Choose the correct options.

1. $y=A\sin \frac{\pi x}{L}\sin \omega t$, has $2$ nodes.
2. $y=A\cos \frac{\pi x}{L}\sin \omega t$, has $2$ antinodes.
3. $y=A\sin \frac{2\pi x}{L}\sin \omega t$, has $2$ antinodes.
4. $y=A\cos \frac{2\pi x}{L}\sin \omega t$, has $2$ nodes.

Q. $y=3sin\pi (\frac{t}{2}-\frac{x}{4})$ represents an equation of a progressive wave, where $t$ is in second and $x$ is in metre. The distance travelled by the wave in $5s$ is

1. $5m$
2. $32m$
3. $8m$
4. $10m$

Q. The length of a sonometer wire between two fixed ends is $1.10m$. Where should the two bridges be placed to divide the wire into three segments whose fundamental frequencies are in the ratio of $1:2:3$?

1. $0.5$ and $0.8$ from left
2. $0.4$ and $0.6$ from left
3. $0.7$ and $0.5$ from left
4. $0.6$ and $0.9$ from left

Q. A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, $y(x,t)=\left(0.01m\sin \right[\left(62.8m^{-1}\right)x\left]\cos \right[\left(628s^{-1}\right)t].$ Assuing $\pi =3.14,$ the correct statement(s) is are

1. The fundamental frequency is $100Hz$
2. The number of nodes is 5
3. The length of the string is $0.25m$
4. The maximum displacement of the midpoint of the string, from its equilibrium position is $0.1m$

Q. In a stationary wave, all particles are at rest at the same time

in every period of oscillation.

1. twice
2. only once
3. thrice

Q. A horizontal stretched string, fixed at two ends, is vibrating in its $5^{th}$ harmonic according to the equation, $y(x,t)=\left(0.10m\right)\sin \left[\right(62.8m^{-1}\left)x\right]\cos \left[\right(628s^{-1}\left)t\right]$. Assuming $\pi =3.14$, the correct statement(s) is/are :

1. The length of the string is $0.25m$
2. The maximum displacement of the midpoint of the string, from its equilibrium position is $0.01m$
3. The fundamental frequency is $100Hz$
4. The number of nodes is $5$

Q. A 40 cm long wire having a mass 3.2 gm and area of cross section $1m{m}^2$ is stretched between the support 40.05 cm apart. In its fundamental mode, it vibrates with a frequency of $\frac{1000}{64}\text{Hz}$. The young's modulus of the wire is ${10}^{x}N/m^2$, then $x$ is.

Q. A string is rigidly tied at two ends and its equation of vibration is given by
$y=\cos 2\pi t\sin 2\pi x$ then minimum length of string is

1. $1m$
2. $\frac{1}{2}m$
3. $5m$
4. $2\pi m$

Q. Two ships are 10 km apart on a line joining south to north. The one farther north is steaming west at $20km{h}^{-1}$. The other is steaming north at $20km{h}^{-1}$. What is their distance of closest approach? How long do they take to reach it?

Q.

difference between wave and particle?

Q. The equation of a wave is $y=5sin(\frac{t}{0.04}-\frac{x}{4})$ where, x is in cm and t is in second. The maximum velocity of the wave will be :

1. $2m{s}^{-1}$
2. $1.25m{s}^{-1}$
3. $1.5m{s}^{-1}$
4. $1m{s}^{-1}$

Q. Which of the following statement is incorrect during propagation of plane progressive mechanical wave?

1. Amplitude of all the particles is equal.
2. All the particles are vibrating in the same phase.
3. Particles of the medium executes SHM.
4. Wave velocity depends upon the nature of the medium.

Q. if you set up the saventh harmonic on a string fixed a both ends, how many nodes and antinodes are set up in it

Q. For the stationary wave $y=4sin\left(\frac{\pi x}{15}\right)cos\left(96\pi t\right)$, the distance between a node and the next antinode is

1. 7.5
2. 15
3. 30
4. 22.5

Q. A generator at one end of a very long string creates a wave given by
$y=\left(6.0cm\right)\cos \frac{\pi }{2}[\left(2.00m^{-1}\right)x+\left(8.00s^{-1}\right)t]$
and a generator at the other end creates the wave
$y=\left(6.0cm\right)\cos \frac{\pi }{2}[\left(2.00m^{-1}\right)x-\left(8.00s^{-1}\right)t]$
For $x\ge 0,$ what is the location of the node having the smallest value of x?

Q. A generator at one end of a very long string creates a wave given by
$y=\left(6.0cm\right)\cos \frac{\pi }{2}[\left(2.00m^{-1}\right)x+\left(8.00s^{-1}\right)t]$
and a generator at the other end creates the wave
$y=\left(6.0cm\right)\cos \frac{\pi }{2}[\left(2.00m^{-1}\right)x-\left(8.00s^{-1}\right)t]$
For $x\ge 0,$ what is the location of the antinode having the third smallest value of x?

Q. 3.In a resonance air column experiment, first and second resonances are obtained at lengths of air columns L1 and L2, the third resonance will be obtained at a length of ---------

Q. A generator at one end of a very long string creates a wave given by
$y=\left(6.0cm\right)\cos \frac{\pi }{2}[\left(2.00m^{-1}\right)x+\left(8.00s^{-1}\right)t]$
and a generator at the other end creates the wave
$y=\left(6.0cm\right)\cos \frac{\pi }{2}[\left(2.00m^{-1}\right)x-\left(8.00s^{-1}\right)t]$
For $x\ge 0,$ what is the location of the node having the second smallest value of x?

Q.

What name has been given to the wave of short duration?

1. Pulse

2. Periodic wave

3. Elastic wave

4. None of these

Q. A standing wave results from the sum of two transverse traveling waves given by
$y_1=0.050\cos (\pi x-4\pi t)$
and $y_2=0.050\cos (\pi x+4\pi t)$
where $x,y_1,$ and $y_2$ are in meters and $t$ is in seconds. (a) What is the smallest positive value of $x$ that corresponds to a node? Beginning at $t=0?$

Q. What characteristics of a point on the string will you use to find the location of the antinode

1. displacement
2. velocity
3. wavelength
4. time

Q. The equation of a progressive wave is $y=0.002\sin 2\pi (2t-0.01x)$. Its wavelength is

1. $20units$
2. $10units$
3. $100units$
4. $200units$

Q.

Two points on string are being observed as a travelling wave passes them. Then point are at $x_1=0$ a $x_2=1m$, the transverse motions of two points are found to be as follows.

$y_1=A\sin \left(3\pi t\right)$ and $y_2=A\sin \left(3\pi t+\frac{\pi }{8}\right)$t is in seconds and y in metre. Mark correct options.

1. Frequency of wave is $3Hz$
2. Frequency of wave is $1.5Hz$
3. Wavelength may be $16m$
4. Wavelength may be $\frac{16}{17}m$

Q. Standing wave name reflects, particles of the medium do not execute SHM.

1. True
2. False