Tag: reflection of waves

Questions Related to reflection of waves

The equation of a stationary wave is $Y=10\sin{\cfrac{\pi x}{4}}\cos{20\pi t}$. The distance between two consecutive nodes in meters is -

  1. 4

  2. 2

  3. 5

  4. 8


Correct Option: A
Explanation:

$Y = 10\sin \dfrac{{\pi x}}{4}\cos \pi t$

At nodles amplitude part is zero.
$\begin{array}{l} \Rightarrow 10\sin  \dfrac { { \pi x } }{ 4 } =0 \ \Rightarrow \dfrac { { \pi x } }{ 4 } =0,\pi ,2\pi  \ \Rightarrow x=0.x=4,x=8 \end{array}$
$\therefore 4$  is distance between two consultative node.
$\therefore$ Option $A$ is correct.

The phase change between incident and reflected sound wave from a free end is

  1. $0$

  2. $\pi $

  3. $3\pi $

  4. $2\pi $


Correct Option: A
Explanation:

At a free and, the wave is reflected as it is with just as change in its direction of propagation 
$y= A  \sin  ( \omega t+kx)$
$y _r= A  \sin  (\omega t-kx)$
phase difference in time domain $= 0$

Regarding open organ pipe, which of following is correct?

  1. Both ends are pressure antinodes

  2. Both ends are displacement nodes

  3. Both ends are pressure nodes

  4. Both (1)and (2)


Correct Option: C
Explanation:

Regarding open pipe both ends are pressure nodes.

So, option $C$ is correct.

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


Correct Option: A
Explanation:

An antinode is a point on the string, where the amplitude at that point is maximum 

The correct option is (a)

Reflection at a free boundary implies

  1. restoring force is zero

  2. restoring force is not zero

  3. applied force is zero

  4. applied force is not zero


Correct Option: A
Explanation:

In a free boundary, the restoring force is always zero

The correct option is (a)

The equation of a progressive wave is given by $y=10 sin (5t-x)$. The wave gets reflected from a open boundary. The equation of the reflected wave is

  1. $y=10 sin (5t-x)$

  2. $y=-10 sin (5t-x)$

  3. $y=10 sin (5t+x)$

  4. $y=10 sin (5t+x+\pi)$


Correct Option: C
Explanation:

In reflection of a wave at open boundaries, the phase reversal dosent take place

The correct option is (c)

A wave of frequency $100$ Hz is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of $10$ cm from the fixed end of the string. The speeds of incident(and reflected) waves are?

  1. $5$ $cms^{-1}$

  2. $10$ $cms^{-1}$

  3. $20$ $cms^{-1}$

  4. $40$ $cms^{-1}$


Correct Option: A
Explanation:

Given frequency $\nu$=100 H. 

Also distance between two successive nodes$=>\dfrac { \lambda  }{ 2 } =10\ \lambda =20\quad cm$
And we know $\nu =n\lambda \ n=\frac { \nu  }{ \lambda  } =\dfrac { 100 }{ 20 } =5\quad cm/s$

A composition string is made up by joining two strings of different masses per unit length $\longrightarrow \mu $ and $4\mu.$ The composite string is under the same tension. A transverse wave pulse : $Y=(6 mm) \sin (5t+40x)$, where '$t$' is in seconds and '$x$' in meters, is sent along the lighter string towards the joint. The joint is at $x=0.$ The equation of the wave pulse reflected from the joint is 

  1. $(2 mm) \sin(5t-40x)$

  2. $(4 mm) \sin(40x-5t)$

  3. $- (2 mm) \sin(5t-40x)$

  4. $(2 mm) \sin(5t-10x)$


Correct Option: C
Explanation:

Since the wave is travelling from low to more dense medium, thus there will be inversion of the reflected wave . Since it travels back from origin, thus $40x$ will become $-40x.$ Also, amplitude of reflected wave is given by:
${ A } _{ r }=\dfrac { Z _{ 1 }-{ Z } _{ 2 } }{ { Z } _{ 1 }+Z _{ 2 } } A.\quad Z=\mu c=\mu \sqrt { \dfrac { T }{ \mu  }  } =\sqrt { \mu T } \ Thus\quad { A } _{ r }=\dfrac { \sqrt { \mu T } -\sqrt { 4\mu T }  }{ \sqrt { \mu T } +\sqrt { 4\mu T }  } A=\dfrac { -1 }{ 3 } A\ $
Thus it become $-6/3=-2$.

Which of the following statement is incorrect superposition of waves?
(i) After superposition frequency,wavelength and velocity of resultant wave remains same
 (ii) After superposition amplitude of resultant wave is equal to amplitude of either wave 
 (iii) Mechanical wave cannot superposed with electromagnetic wave
 (iv) For superposition two waves should have equal wavelength,frequency and amplitude

  1. I & III Only

  2. I & II Only

  3. I,II, & III Only

  4. II & IV Only


Correct Option: A

The wavelength of the first line of Lyman series is $\lambda$. The wavelength of the first line in Paschen series is ________.

  1. $108/7$

  2. $27/5$

  3. $7/108$

  4. $5/27$


Correct Option: A
Explanation:
Formula for Lyman series is:
Where, n = 2,3,4,5,.....
Where, R = Rydbergg constant,
$\dfrac{1}{\lambda}=R\left(\dfrac{1}{1^2}-\dfrac{1}{2^2}\right)$ and
 Paschen series in $\lambda _1$,
$\Rightarrow \dfrac{1}{\lambda _1}=R\left(\dfrac{1}{3^2}-\dfrac{1}{4^2}\right)$

$\Rightarrow \dfrac{\lambda _1}{\lambda}=\dfrac{\dfrac{3}{4}}{\dfrac{7}{16\times 9}}$

$\Rightarrow \lambda _1=\dfrac{3}{4}\times \dfrac{16\times 9}{7}\lambda$

$\Rightarrow \lambda _1=\dfrac{108}{7}\lambda$.