Reflection from a Fixed End

Q. A heavy ball of mass $M$ is suspended from the ceiling of a car by a light string of mass $m(m<<M)$. When the car is at rest, the speed of transverse waves in the string is $60{\text{ms}}^{-1}$. When the car has acceleration $a$, the wave-speed increases to $60.5{\text{ms}}^{-1}$. The value of $a$, in terms of gravitational acceleration $g$, is closest to:

1. $\frac{g}{20}$
2. $\frac{g}{5}$
3. $\frac{g}{10}$
4. $\frac{g}{30}$

Q. A wave travels on a light string. The equation of the wave is $y=Asin(kx+wt+{30}^{\circ }+{180}^{\circ })$, it is reflected from a heavy string tied to an end of the light string at x= 0. If 64% of the incident energy is reflected then what is the equation of the reflected wave?

1. $y=Asin(kx-wt+{30}^{\circ })$
2. $y=Asin(kx+wt+{30}^{\circ })$
3. $y=0.8Asin(kx-wt+{30}^{\circ })$
4. $y=0.8Asin(kx+wt+{30}^{\circ })$

Q.

The equation of a wave travelling on a string is $y=\left(0.10mm\right)sin\left[\right(31.4m^{-1})x+(314s^{-1}\left)t\right].$ (a) In which direction does the wave travel ? (b) Find the wave speed, the wavelength and the frequency of the wave. (c) What is the maximum displacement and the maximum speed of a portion of the string ?

Q.

What is the wavefront of the light waves?

Q.

A wave travelling on a string at a speed of $10m{s}^{-1}$ causes each particle of the string to oscillate with a time period of 20 ms. (a) What is the wavelength of the wave ? (b) If the displacement of a particle is 1.5 mm at a certain instant, what will be the displacement of a particle 10 cm away from it at the same instant ?

Q. If tension is increased by $4\%$ in vibrating string, then percentage change in speed of wave will be

1. $1\%$
2. $2\%$
3. $3\%$
4. $4\%$

Q.

Two long strings A and B, each having linear mass density $1.2\times {10}^{-2}kg{m}^{-1},$ are stretched by different tensions 4.8 N and 7.5 N respectively and are kept parallel to each other with their left ends at x = 0. Wave pulses are produced on the strings at the left ends at t = 0 on string A and at t = 20 ms on string B. When and where will the pulse on B overtake that on A ?

Q.

A string of length 40 cm and weighing 10 g is attached to a spring at one end to a fixed wall at the other end. The spring has a spring constant of $160N{m}^{-1}$ and is stretched by 1.0 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring ?

Q. Particle displacements (in $\text{cm}$) in a standing wave are given by $y(x,t)=2\sin \left(0.1\pi x\right)\cos \left(100\pi t\right)$. The distance between a node and the next antinode is

1. $2.5\text{cm}$
2. $5.0\text{cm}$
3. $7.5\text{cm}$
4. $10.0\text{cm}$

Q. A string of length $40\text{cm}$ and linear mass density $0.80\text{g/cm}$ is fixed at both ends and kept under a tension of $32\text{N}$. A wave pulse is produced near one of the ends at $t=0$, as shown in the figure, which makes periodic motion between the ends. What is the time after which the string will have the same shape shown in the figure?

1. After $0.04\text{sec}$
2. After $0.03\text{sec}$
3. After $0.06\text{sec}$
4. After $0.05\text{sec}$

Q.

In the figure, A is an incident pulse and a, b, c, d are the possible forms of the reflected pulse. Tick the correct answer.

1. a is after reflection form a rigid wall
2. b is after reflection from a yielding surface
3. c is after reflection from a yielding surface
4. d is after reflection from a rigid wall

Q. A sinusoidal wave represented by $y_i=0.3\cos (2x-40t)$ is travelling along a string towards a fixed end at $x=0$. Then, the equation of the reflected wave will be:-
(Assume there is no loss of energy at the boundary)

1. $0.3\cos (2x+40t+\frac{\pi }{2})$
2. $0.3\cos (2x-40t+\frac{\pi }{2})$
3. $0.3\cos (2x-40t+\pi )$
4. $0.3\cos (2x+40t-\pi )$

Q. On the basis of Huygens' wave theory of light prove that velocity of light in a rarer medium is greater than velocity of light in a denser medium.

Q. $P$ is the junction of two wires $\text{A}$ and $\text{B}$. $\text{B}$ is made of steel and is thicker, while $\text{A}$ is made of aluminum and is thinner as shown in the figure$(i.e.{\mu }_B>{\mu }_A)$. If a wave pulse as shown in the figure approaches $P$, the reflected and transmitted waves from $P$ are respectively:

1. 
2. 
3. 
4. 

Q. $P$ is the junction of two wires $\text{A}$ and $\text{B}$. $\text{B}$ is made of steel and is thicker, while $\text{A}$ is made of aluminum and is thinner as shown in the figure. If a wave pulse as shown in the figure approaches $P$, the reflected and transmitted waves from $P$ are respectively:

1. 
2. 
3. 
4. 

Q. A traveling wave in a stretched string is described by the equation, $y=A\sin (kx+t)$. The maximum particle velocity is

1. A
2. $k$
3. $Ak$
4. none of the above

Q. A weight of 5 kg is required to produce the fundamental frequency of a sonometer wire. What weight is required to produce its octave?

1. 32
2. 26
3. 20
4. none of the above

Q.

$y=15\sin (660t–0.02x)$can be used to calculate the equation of a progressive wave. The wave has a frequency of

1. $330Hz$

2. $342Hz$

3. $365Hz$

4. $660Hz$

Q. The equation of a plane progressive wave is $y=0.9sin4\pi [t-\frac{x}{2}]$. When it is reflected at a rigid support, its amplitude becomes $\frac{2}{3}$ of its previous value. The equation of the reflected wave is

1. $y=0.6sin4\pi [t+\frac{x}{2}]$
2. $y=-0.6sin4\pi [t+\frac{x}{2}]$
3. $y=-0.9sin8\pi [t-\frac{x}{2}]$
4. $y=-0.9sin4\pi [t+\frac{x}{2}]$

Q.

A string of length $ 20 cm $and linear mass density $ 0.40 gc{m}^{-1}$ is fixed at both ends and is kept under a tension of $ 16 N$. A wave pulse is produced at $ t=0$ near an end as shown in figure (below), which travels towards the other end.

(a) When will the string have the shape shown in the figure again?

(b) Sketch the shape of the string at a time half of that found in part (a).

20em 

Q. The equation for a wave travelling in x - direction on a string is
$y=\left(3.0cm\right)sin\left[\right(3.14c{m}^{-1})x-(314s^{-1}\left)t\right]$ Find the acceleration of a particle at x = 6.0 cm at time t = 0.11 s.

Q. When a wave is reflected from a rarer medium, change in phase is

1. $\pi$
2. $0.5\pi$
3. $0.75\pi$
4. $0$

Q. Equation of plane progressive wave is given by $y=0.6sin2\pi (t-\frac{x}{2})$. On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is

1. $y=0.6sin2\pi (t+\frac{x}{2})$
2. $y=-0.4sin2\pi (t+\frac{x}{2})$
3. $y=-0.4sin2\pi (t-\frac{x}{2})$
4. $y=0.4sin2\pi (t+\frac{x}{2})$

Q. An open pipe of length 24 cm is in resonance with a frequency 660 Hz. The radius of pipe is : (V=330 ms${}^{-1}$)

1. 0.83 cm
2. 3 cm
3. 2 cm
4. 3.5 cm

Q. A wave travels on a light string. The equation of the wave is $Y=A\sin (kx-\omega t+30+180)$. It is reflected from a heavy string tied to an end of the light string at x = 0. If 64% of the incident energy is reflected the equation of the reflected wave is

1. $Y=0.8A\sin (kx-\omega t+30+180)$
2. $Y=0.8A\sin (kx+\omega t+30+180)$
3. $Y=0.8A\sin (kx+\omega t-30)$
4. $Y=0.8A\sin (kx+\omega t+30)$

Q.

A string of length 0.4 m and mass ${10}^{-2}$ kg is tightly clampled at its ends. The tension in the string is 1.6 N. identical wave pulses are produced at one end at equal intervals of time ∆t. The minimum value of ∆t, which allows constructive interference between succesive pulses, is :

1. 0.05 s

2. 0.10 s

3. 0.20 s

4. 0.40 s

Q. In Young's double slit experiment, the intensity on the screen at a point where path differences is $\lambda$ is $K$. What will be the intensity at the point where path difference is $\frac{\lambda }{4}$ ?

1. $\frac{K}{4}$
2. $\frac{K}{2}$
3. $K$
4. Zero

Q. $A$ source $S$ and a detector $D$ are placed at a distance d apart. A big cardboard is placed at a distance $\sqrt{2}$d from the source and the detector as shown in figure. The source emits a wave of wavelength = $d/2$ which is received by the detector after reflection from the cardboard. It is found to be in phase with the direct wave received from the source. By what minimum distance should the cardboard be shifted away so that the reflected wave becomes out of phase with the direct wave?

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

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

Q. If the two waves represented by $y_1=4sin\omega t$ and $y_2=3sin(\omega t+\pi /3)$ interfere at a point, the amplitude of the resulting wave will be about

1. $7$
2. $3.5$
3. $6$
4. $5$