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On adding two sine waves that are exactly the same, what would be the result?
  • a)
    an identical sine wave with half the amplitude
  • b)
    an identical sine wave with double the frequency
  • c)
    an identical sine wave
  • d)
    an identical sine wave with double the amplitude
Correct answer is option 'D'. Can you explain this answer?
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On adding two sine waves that are exactly the same, what would be the ...
According to the Principle of Superposition, if the particle of a medium is given an order (i.e. of oscillating sinusoidally) and then another order (similar or different), the particle simply adds the two orders vectorially (i.e. by vector method), and then oscillates by the amplitude of the resultant vector.
So if the particle of a medium is given two similar orders (i.e., both the sine waves having the same amplitude, say A) then the particle will oscillate with an amplitude, 2A, i.e., the amplitude will be doubled.
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On adding two sine waves that are exactly the same, what would be the ...
According to the Principle of Superposition, if the particle of a medium is given an order(i.e., of oscillating sinusoidally) and then another order (similar or different) , the particle simply adds the two orders vectorially (i.e., by vector method) , and then oscillates by the amplitude of the resultant vector.
So if the particle of a medium is given two similar orders (i.e., both the sine waves having the same amplitude, say A) then the particle will oscillate with an amplitude, 2A, i.e., the amplitude will be doubled.
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Attempt All sub parts from each question.Galileo’s Isochronous Pendulum: Galileo observed a lamp swinging from ceiling at Pisa cathedral ceiling. He was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same. So, he concluded that the oscillations are isochronous. Anyhow, it was proved by advanced experimentation that the isochronism of simple pendulum is correct within 1% under the 30° of amplitude. It is confirmed that the period changes less than 1% until the amplitude is 30°. On the other hand, the period increased by more than 10% when the amplitude became larger than 80°. At the end of his life he devised a scheme for using a pendulum to regulate a mechanical clock. However, the first reliable pendulum clock was only demonstrated by Huygens 15 years after Galileo's death.Q. Isochronism of simple pendulum is within acceptable limit as long as the amplitude is under

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On adding two sine waves that are exactly the same, what would be the result?a)an identical sine wave with half the amplitudeb)an identical sine wave with double the frequencyc)an identical sine waved)an identical sine wave with double the amplitudeCorrect answer is option 'D'. Can you explain this answer?
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