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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
In an organ pipe whose one end is at $x = 0$, the pressure is expressed by $p = {p_0}\cos \frac{{3\pi x}}{2} \,\,sin\,\, 300\pi t$  where $x$ is in meter and $t$ in $sec$. The organ pipe can be
  • A
    closed at one end, open at another with length $= 0.5m$
  • B
    open at both ends, length $= 1m$
  • ✓
    closed at both ends, length $= 2m$
  • D
    closed at one end, open at another with length = $\frac{2}{3} m$ 
✓

Answer

Correct option: C.
closed at both ends, length $= 2m$
c
Pressure is maximum at closed end and minimum at open end.

At $x=0 m, \cos \frac{3 \pi x}{2}=\cos \frac{3 \pi \times 0}{2}=1$

Thus $p$ is maximum, so $x=0$ is a closed end

At $x=2 m \cos \frac{3 \pi x}{2}=\cos \frac{3 \pi \times 2}{2}=-1$

Thus $|p|$ is maximum at $x=2 m,$ so $x=2$ is also a closed end.

Hence the given organ pipe is closed at both ends and length of the pipe is $2 m$

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