Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of $6\, beats/s$ when both the wires oscillate together would be

Beats are produced by two waves $y_1 = a\, sin\, (1000\, \pi t)$ and $y^2 = a\, sin\, (998\, \pi t)$ The number of beats heard per second is

Three waves of equal frequency having amplitudes $10\,\mu m$, $4\,\mu m$, $7\,\mu m$ arrive at a given point with successive phase difference of $\pi /2$, the amplitude the resulting wave in $\mu m$ is given by

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

Figure shows the wave $y = A\,sin\,(\omega t -kx)$ .What is the magnitude of slope of the curved at $B$

 Two cars $A$ and $B$ are moving in the same direction with speeds $36\,km/hr$ and $54\,km/hr$ respectively. Car $B$ is ahead of $A$. If $A$ sounds horn of frequency $1000\,Hz$ and the speed of sound in air is $340\,m/s$, the frequency of sound received by the driver of car $B$ is .................. $\mathrm{Hz}$