Questions in waves

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Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is $a$ and the phase of A is ahead by $\frac{\pi }{3}$ than that of B and the distance AP is greater than BP by 50 cm. Then the resultant amplitude at the point P will be, if the wavelength is 1 meter
Coherent sources are characterized by the same
The minimum intensity of sound is zero at a point due to two sources of nearly equal frequencies, when
Two sound waves (expressed in CGS units) given by ${{y}_{1}}=0.3\sin \frac{2\pi }{\lambda }(vt-x)$ and ${{y}_{2}}=0.4\sin \frac{2\pi }{\lambda }(vt-x+\theta )$ interfere. The resultant amplitude at a place where phase difference is $\pi /2$ will be
If two waves having amplitudes $2A$ and $A$ and same frequency and velocity, propagate in the same direction in the same phase, the resulting amplitude will be
The intensity ratio of two waves is 1 : 16. The ratio of their amplitudes is
Out of the given four waves (1), (2), (3) and (4).
$y=a\sin (kx+\omega t)$ ......(1)
$y=a\sin (\omega t-kx)$ ......(2)
$y=a\cos (kx+\omega t)$ ......(3)
$y=a\cos (\omega t-kx)$ ......(4)
emitted by four different sources ${{S}_{1}},\,{{S}_{2}},\,{{S}_{3}}$ and ${{S}_{4}}$ respectively, interference phenomena would be observed in space under appropriate conditions when
Two waves of same frequency and intensity superimpose with each other in opposite phases, then after superposition the
The superposing waves are represented by the following equations : ${{y}_{1}}=5\sin 2\pi (10\,t-0.1x)$, ${{y}_{2}}=10\sin 2\pi (20\,t-0.2x)$. Ratio of intensities $\frac{{{I}_{\max }}}{{{I}_{\min }}}$ will be
The displacement of a particle is given by $x=3\sin (5\pi \,t)+4\cos (5\pi \,t)$. The amplitude of the particle is

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