Tag: standing waves in strings

Questions Related to standing waves in strings

A standing wave is represented by an equation $y= 20 sin (50 \pi t )cos (10 \pi x)$. The frequency of the wave is

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. 20 Hz

  2. 50 Hz

  3. 25 Hz

  4. 10 Hz

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Correct Option: C
Explanation:

The equation of a stationary wave is $y= 2A sin \omega t cos K x$. Comparing this equation with the equation given in the problem, we have
$2 \pi f = 50 \implies f = 25 Hz$

The correct option is (c)

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

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. All the particles are vibrating in the same phase.

  2. Amplitude of all the particles is equal.

  3. Particles of the medium executes SHM.

  4. Wave velocity depends upon the nature of the medium.

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Correct Option: A
Explanation:

During propagation of a plane progressive mechanical wave all the particles are vibrating with different phases.
While all other statement are correct.

A standing wave is given by the equation $x=10 sin 5\pi t cos 3 x$. The amplitude of the wave will be

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. a constant at all times

  2. will be increasing as t increases

  3. will be decreasing as t increases

  4. will fluctuate at x increases

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Correct Option: D
Explanation:

The amplitude of the stationary wave is $10 cos 3 x$ and this fluctuates as x increases

The correct option is (d)

A standing wave is represented by an equation $y= 10 sin 50 \pi t cos 10 \pi x$. The distance between adjacent nodes of the wave is

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. 0.5 m

  2. 0.2 m

  3. 0.1 m

  4. 0.3 m

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Correct Option: C
Explanation:

At nodes, displacement $y=0$

For first node:
$\cos { \left( 10\pi x \right) =0\quad =\cos { \left( \cfrac { \pi  }{ 2 }  \right)  }  } \ \therefore \quad 10\pi x=\cfrac { \pi  }{ 2 } \ x=\cfrac { 1 }{ 20 } $
For second node:
$\cos { \left( 10\pi x \right) =0\quad =\cos { \left( \cfrac { 3\pi  }{ 2 }  \right)  }  } \ \therefore \quad 10\pi x=\cfrac { 3\pi  }{ 2 } \ x=\cfrac { 3 }{ 20 } $
$\therefore$ distance between them $=\cfrac { 3 }{ 20 } -\cfrac { 1 }{ 20 } \ \quad \quad =\cfrac { 1 }{ 10 } =0.1m$

The frequency of a sound wave is 250 Hz and its wavelength is 100 cm. The distance travelled by a sound wave in the time taken to produce 100 waves is ________.

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. 100m

  2. 200m

  3. 300m

  4. 400m

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Correct Option: A
Explanation:

$v = 250 \times 1 = 250  m  s^{-1}$
$t = \displaystyle \frac{100}{250} s = 0.45$
Distance travelled by wave in the time taken to produce 100 waves $=$ v $\times$ time
$= $ 250 $\times$ 0.45
$=112.5m \approx 100m$

The waves in which the particles of the medium travel in the same direction as the waves are

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. linear waves

  2. longitudinal waves

  3. transverse waves

  4. electromagnetic waves

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Correct Option: B
Explanation:

The waves in which the displacement of the medium is in the same direction as, or the opposite direction to the direction of the propagation of the wave, are called lognitudinal waves. Ex$:-$ Sound waves, sewmic waves

While $:-$ 
The wave in which the displacement of the medium are at right angles to the direction of propogation, are called trensverse waves.
Ex$:-$ Electromagnetic waves, ripple on water surface.
Option (B) is the correct answer

Which of the following functions represent a traveling wave ?

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. $({ x-vt })^{ 2 }$

  2. $({ x-vt })^{ 3 }$

  3. ${ 2 }^{ -(x-vt)^{ 2 } }$

  4. ${ e }^{ (x-vt) }$

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Correct Option: D

The equation of the stationary wave is
$y=2A\quad sin(\cfrac { 2\pi ct }{ \lambda  } )cos(\cfrac { 2\pi x }{ \lambda  } )$
Which of the following statement (s) is wrong?

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. The unit of ct is same as that of $\lambda$

  2. The unit of x is same as that of $\lambda$

  3. The unit of $2\pi t$ is same as that of $2\pi x/\lambda t$

  4. The unit of $c/\lambda$ is same as that of $x/\lambda$

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Correct Option: C,D
Explanation:

$y=2Asin(\dfrac{2\pi ct}{\lambda}). cos(\dfrac{2\pi x}{\lambda})$


The unit of $\lambda $ and $x$ is $m$


The unit of $ct$ is $m$

The unit of $2\pi t$ is $s$.

The unit of $2\pi x/\lambda t$ is $s^{-1}$

The unit of $\dfrac{c}{\lambda}$ is $s^{-1}$

The unit of $x/\lambda$ is unit less.

The wrong statement is C and D both.

In a plane progressive harmonic wave, $V _{P}$ is the maximum particle speed and $V$ is the wave speed. If amplitude of wave is less than $\lambda/ 2\pi$, then

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. $V = V _{P}$

  2. $V > V _{P}$

  3. $V _{P} < V$

  4. Unpredictable

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Correct Option: C

Standing waves are produced in $10m$ long stretched wire. If wire vibrates in five segments and wave velocity is $20m/s$, then the frequency is $(in\ Hz)$

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. $5$

  2. $10$

  3. $15$

  4. $20$

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Correct Option: A