The amplitude of a wave represented by displacement equation $y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be

Two waves of sound having intensities $I$ and $4I$ interfere to produce interference pattern. The phase difference between the waves is $\pi /2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is

A string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of transverse wave along the string at a distance $'x'$ from the free end will be

Two waves represented by, $y_1 = 10\,sin\, 200\pi t$ , ${y_2} = 20\,\sin \,\left( {2000\pi t + \frac{\pi }{2}} \right)$ are superimposed at any point at a particular instant. The amplitude of the resultant wave is

Fundamental frequency of a sonometer wire is $n$ . If the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is

A transverse wave is described by the equation $y = {y_0}\sin 2\pi \left( {ft - \frac{x}{\lambda }} \right)$. The maximum particle velocity is equal to four times wave velocity if