a man is watching two trains one leaving and the other

A man is watching two trains, one leaving and the other coming in with equal speeds of $$4\,m/\sec.$$ If they sound their whistles, each of frequency $$240\,Hz,$$ the number of beats heard by the man (velocity of sound in air $$= 320\,m/\sec$$ ) will be equal to

A. 6

B. 3

C. 0

D. 12

Answer : 6

Solution :
Waves mcq solution image

Frequency of Sound heard by the man from approaching train.
$${n_a} = n\left( {\frac{v}{{v - {v_s}}}} \right) = 240\left( {\frac{{320}}{{320 - 4}}} \right) = 243\,Hz$$
Frequency of sound heard by the man from receding train $${n_r} = n\left( {\frac{v}{{v + {v_s}}}} \right) = 240\left( {\frac{{320}}{{320 + 4}}} \right) = 237\,Hz$$
Hence, number of beats heard by man per $$\sec$$
$$ = {n_a} - {n_r} = 243 - 237 = 6$$

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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. $$2\,f$$

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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. $$ - a\sin \left( {k\,x - \omega t} \right)$$

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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. $$300\left( {\frac{{2\,\rho - 1}}{{2\,\rho }}} \right)$$

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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

A man is watching two trains, one leaving and the other coming in with equal speeds of $$4\,m/\sec.$$ If they sound their whistles, each of frequency $$240\,Hz,$$ the number of beats heard by the man (velocity of sound in air $$= 320\,m/\sec$$ ) will be equal to

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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

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