Tag: reflection of waves

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Questions Related to reflection of waves

Multiple choice physics wave motion 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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice physics wave motion reflection of waves

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

  1. $0$
  2. $\pi $
  3. $3\pi $
  4. $2\pi $
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $= 0$

Multiple choice physics wave motion reflection of waves

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)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Regarding open pipe both ends are pressure nodes.

So, option $C$ is correct.

Multiple choice physics wave motion reflection of waves

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

The correct option is (a)

Multiple choice physics wave motion reflection of waves

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a free boundary, the restoring force is always zero

The correct option is (a)

Multiple choice physics wave motion reflection of waves

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. $y=10 sin (5t+x+\pi)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

The correct option is (c)

Multiple choice physics wave motion reflection of waves

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. $40$ $cms^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given frequency $\nu$=100 H. 

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

Multiple choice physics wave motion reflection of waves

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. $(2 mm) \sin(5t-10x)$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $-6/3=-2$.

Multiple choice physics wave motion reflection of waves

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement (i) is incorrect because the resultant wave's amplitude changes, though frequency/wavelength remain the same. Statement (iii) is incorrect because mechanical and electromagnetic waves can superpose (e.g., light interacting with a medium). Statement (ii) is incorrect as the resultant amplitude depends on phase. Statement (iv) is incorrect as superposition occurs for waves of different properties. Given the options, (i) and (iii) are the most clearly incorrect statements regarding the fundamental principles of superposition.

Multiple choice physics wave motion reflection of waves

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. $5/27$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $\lambda _1$,
$\Rightarrow \dfrac{1}{\lambda _1}=R\left(\dfrac{1}{3^2}-\dfrac{1}{4^2}\right)$

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

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

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