JEE PHYSICS MCQ: WAVES

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A standing wave is maintained in a homogeneous string of cross-sectional area

s

and density

\rho

. It is formed by the superposition of two waves travelling in opposite directions given by the equation

y_1=a \sin (\omega t-k x)

and

y_2=2 a \sin (\omega t+k x)

. The total mechanical energy confined between the sections corresponding to the adjacent antinodes is

View answer and explanation

Correct option: C

\frac{5 \pi s p \omega^2 a^2}{2 k}

The correct answer is C. The total mechanical energy is calculated by summing the energy densities of the two waves and multiplying by the volume between adjacent antinodes.

More Questions from WAVES

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The source of sound generating a frequency of

3\,\,kHz

reaches an observer with a speed of

0.5

times, the velocity of sound in air. The frequency heard by the observer is A source of sound emits waves with frequency

f\mathrm{ }Hz

and speed

V\mathrm{ }m/sec

. Two observers move away from this source in opposite directions each with a speed

0.2\,\,V

relative to the source. The ratio of frequencies heard by the two observers will be Assertion: The wave function of a pulse is given by

y = \frac{3}{{{{\left( {2x + 3t} \right)}^2} + 4}},

it propagates in

(– \mathrm{ve}) \,x

-direction.
Reason: The given wave function is of the form

y = f(kx +\omega t),

which represent a wave travelling in negative

X

-direction. In the fundamental mode, time taken by the wave to reach the closed end of the air filled pipe is

0.01\,\,s

. the fundamental frequency is A rope

5 \mathrm{~m}

long has a total mass of

245 \mathrm{~g}

. It is stretched with a constant tension of

1 \mathrm{~kg}

wt. If it is fixed at one end and shaken by hand at the other end, what frequency of shaking will make it break up into three vibrating segments? Take

g=980 \mathrm{~cm} \mathrm{~s}^{-2}

. If

T

is the reverberation time of an auditorium of volume

V

then