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Waves Test - 40

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Waves Test - 40
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Weekly Quiz Competition
  • Question 1
    1 / -0
    Identify the correct statement:
    Solution

  • Question 2
    1 / -0
    A stationary wave is represented by the equation, $$y = 3 \cos(x/8) \sin(15t)$$ where $$x$$ and $$y$$ are in $$cm$$ and $$t$$ is in $$seconds$$. The distance between the consecutive nodes is (in $$cm$$):
    Solution
    Distance between two consecutive nodes=$$\dfrac { \lambda  }{ 4 } $$
    $$\dfrac { \lambda  }{ 4 } =\dfrac { 2\pi  }{ K } \times \dfrac { 1 }{ 4 } $$
    From, $$y=3\cos { \left( \dfrac { x }{ 8 }  \right)  } \sin { \left( 15t \right)  } \\ K=\dfrac { 1 }{ 8 } \\ \therefore \dfrac { \lambda  }{ 4 } =\dfrac { 2\pi  }{ K } \times \dfrac { 1 }{ 4 } =\dfrac { 2\pi \times 8 }{ 4 } =4\pi $$
    Hence distance between the consecutive nodes is $$4\pi $$cm
  • Question 3
    1 / -0
    Two points on a travelling wave having frequency $$500 Hz$$ and velocity $$300{ m }/{ s }$$ are $${ 60 }^{ o }$$ out of phase, then the minimum distance between the two points is
    Solution
    Wavelength of the wave is: 
    $$\lambda = \dfrac{v}{f} = \dfrac{300}{500} = 0.6\ m$$

    $$360^o$$ phase difference corresponds to a distance of $$1$$ wavelength or
    $$360^o$$ phase difference corresponds to a distance of $$ 0.6\ m$$ 
    $$60^o$$ phase difference corresponds to a distance of $$ 0.6/6 = 0.1\ m$$ 
  • Question 4
    1 / -0
    Stethoscope of doctors for finding quality, strength and frequency of human heart beat is based on the principle of
    Solution
    Stethoscope of doctors for finding quality, strength and frequency of human heart beat is based on the principle of multiple reflection. In stethoscope, sound is received by chest piece and sent to the earpieces by multiple reflecting through a long tube
  • Question 5
    1 / -0
    A weight of 5 kg is required to produce the fundamental frequency of a sonometer wire. What weight is required to produce its octave?
    Solution
    In a sonometer wire,
    $$f \propto \sqrt{T}$$
    $$f_{octave}=2f_{fundamental}$$
    $$T_{octave}=4T_{fundamental}$$
    $$M_{octave}g=4m_{fundamental}$$
    $$M_{octave}=20kg$$
  • Question 6
    1 / -0
    On watching the graphical representation of different waves which of the following does not have energy carrying capacity
    Solution
    standing wave patterns are produced as the result of the repeated interference of two waves of identical frequency while moving in opposite directions along the same medium. so since the waves are stationary the energy will not be propogated.
    the answer is B.
  • Question 7
    1 / -0
    A stationary wave is a multidimensional variant depending on
    Solution
    A stationary wave is a multidimensional variation which oscillates in time but whose peak amplitude profile dose not move in space.
    Equ of stationary wave : $$y=A\sin(wt)\cos(Kr)$$
    It depends on both time and position axis.

    $$\therefore $$  Option (C) is correct.
  • Question 8
    1 / -0
    The amplitude of resulting wave dues to superposition of $$y_1 = A sin (t -kx)$$ & $$y_2 = A sin (t -kx + \delta)$$ is
    Solution

  • Question 9
    1 / -0
     The amplitude of resulting wave dues to superposition of $$y_1 = A sin (t -kx)$$ & $$y_2 = A sin (t- kx + \delta)$$ is
    Solution

  • Question 10
    1 / -0
    Sum of two mechanical waves travelling in any direction (having the same frequency),
    Solution
    sum of two mechanical waves travelling in any direction with same frequency can be done by using phasor diagram.
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