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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
Equation of a progressive wave is given by $y = 4\sin \left\{ {\pi \left( {\frac{t}{5} - \frac{x}{9}} \right) + \frac{\pi }{6}} \right\}$. Then which of the following is correct
  • A
    $v = 5\,m/\sec $
  • ✓
    $\lambda = 18\,m$
  • C
    $a = 0.04\,m$
  • D
    $n = 50\,Hz$
✓

Answer

Correct option: B.
$\lambda = 18\,m$
b
(b) From the given equation amplitude $a = 0.04m$ 

Frequency $ = \frac{{{\rm{Co}} - {\rm{efficient of t}}}}{{2\pi }}$

 $ = \frac{{\pi /5}}{{2\pi }} = \frac{1}{{10}}Hz$ 

Wave length $\lambda = \frac{{2\pi }}{{{\rm{Co}} - {\rm{efficient}}\;of\;x}}$

$ = \frac{{2\pi }}{{\pi /9}}=18m.$

Wave speed $v = \frac{{{\rm{Co - efficient of }}t}}{{{\rm{Co - efficient of }}x}}$ 

$ = \frac{{\pi /5}}{{\pi /9}} = 1.8m/s.$

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