Question

The number of possible natural oscillation of air column in a pipe closed at one end of length $$85\,cm$$  whose frequencies lie below $$1250\,Hz$$   are: (velocity of sound $$ = 340\,m{s^{ - 1}}$$  )

A. 4
B. 5
C. 7
D. 6  
Answer :   6
Solution :
In case of closed organ pipe frequency,
$$\eqalign{ & {f_n} = \left( {2n + 1} \right)\frac{v}{{4l}} \cr & {\text{for}} \cr & n = 0,{f_0} = 100\,Hz \cr & n = 1,{f_1} = 300\,Hz \cr & n = 2,{f_2} = 500\,Hz \cr & n = 3,{f_3} = 700\,Hz \cr & n = 4,{f_4} = 900\,Hz \cr & n = 5,{f_5} = 1100\,Hz \cr & n = 6,{f_6} = 1300\,Hz \cr} $$
Hence possible natural oscillation whose frequencies $$ < 1250\,Hz = 6\left( {n = 0,1,2,3,4,5} \right)$$

Releted MCQ Question on
Oscillation and Mechanical Waves >> Waves

Releted Question 1

A cylindrical tube open at both ends, has a fundamental frequency $$'f'$$ in air. The tube is dipped vertically in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column in now

A. $$\frac{f}{2}$$
B. $$\frac{3\,f}{4}$$
C. $$f$$
D. $$2\,f$$
View Answer
Releted Question 2

A wave represented by the equation $$y = a\cos \left( {k\,x - \omega t} \right)$$    is superposed with another wave to form a stationary wave such that point $$x = 0$$  is a node. The equation for the other wave is

A. $$a\sin \left( {k\,x + \omega t} \right)$$
B. $$ - a\cos \left( {k\,x - \omega t} \right)$$
C. $$ - a\cos \left( {k\,x + \omega t} \right)$$
D. $$ - a\sin \left( {k\,x - \omega t} \right)$$
View Answer
Releted Question 3

An object of specific gravity $$\rho $$ is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is $$300\,Hz.$$  The object is immersed in water so that one half of its volume is submerged. The new fundamental frequency in $$Hz$$  is

A. $$300{\left( {\frac{{2\,\rho - 1}}{{2\,\rho }}} \right)^{\frac{1}{2}}}$$
B. $$300{\left( {\frac{{2\,\rho }}{{2\,\rho - 1}}} \right)^{\frac{1}{2}}}$$
C. $$300\left( {\frac{{2\,\rho }}{{2\,\rho - 1}}} \right)$$
D. $$300\left( {\frac{{2\,\rho - 1}}{{2\,\rho }}} \right)$$
View Answer
Releted Question 4

A wave disturbance in a medium is described by $$y\left( {x,t} \right) = 0.02\cos \left( {50\,\pi t + \frac{\pi }{2}} \right)\cos \left( {10\,\pi x} \right)$$        where $$x$$ and $$y$$ are in metre and $$t$$ is in second

A. A node occurs at $$x = 0.15\,m$$
B. An antinode occurs at $$x = 0.3\,m$$
C. The speed wave is $$5\,m{s^{ - 1}}$$
D. The wave length is $$0.3\,m$$
View Answer

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