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Waves

Question
CBSEENPH11020487
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The displacement y of a particle in a medium can be expressed as y = 10−6 sin(110t + 20 x + π/4) m, where t is in seconds and x in a meter. The speed of the wave is

  • 2000 m/s

  • 5 m/s

  • 20 m/s

  • 5π m/s

Solution

B.

5 m/s

As given,
straight y space equals 10 to the power of negative 6 end exponent space sin space open parentheses 100 straight t space plus 20 straight x plus straight pi over 4 close parentheses ........ (i)
Comparing it with

y = a sin(ωt + kx + φ) ............. (ii)
we find ω = 100 rad/sec, k = 20 per metre
straight v equals fraction numerator space straight omega over denominator straight k end fraction space equals space 100 over 20 space equals space 5 space straight m divided by straight s

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