JEE Advanced PYQ Beats, Interference and Superposition of Waves

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Q 1 :

A vibrating string of certain length $l$ under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is [2008]

344
336
117.3
109.3

(1)

With increase in tension, the frequency produced by string increases. As the beats/sec decreases therefore frequency of tuning fork

$f = 3 (\frac{v}{4 l}) + 4 = 3 (\frac{340}{4 \times 0.75}) + 4 = 344 Hz$

Q 2 :

When two progressive waves $y_{1} = 4 \sin (2 x - 6 t)$ and $y_{2} = 3 \sin (2 x - 6 t - \frac{π}{2})$ are superimposed, the amplitude of the resultant wave is [2010]

(5)

Here the phase difference between the two waves, $ϕ = \frac{π}{2}$

$Resultant amplitude, A = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos ϕ}$

$= \sqrt{4^{2} + 3^{2} + 2 \times 4 \times 3 \times \cos \frac{π}{2}}$

$= \sqrt{16 + 9 + 0} = 5$

Topic Question Set

Q 2 :

When two progressive waves $y_{1} = 4 \sin (2 x - 6 t)$ and $y_{2} = 3 \sin (2 x - 6 t - \frac{π}{2})$ are superimposed, the amplitude of the resultant wave is [2010]

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Topic Question Set

Q 2 : When two progressive waves y1=4sin(2x-6t) and y2=3sin(2x-6t-π2) are superimposed, the amplitude of the resultant wave is [2010]

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Q 2 :

When two progressive waves $y_{1} = 4 \sin (2 x - 6 t)$ and $y_{2} = 3 \sin (2 x - 6 t - \frac{π}{2})$ are superimposed, the amplitude of the resultant wave is [2010]