Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent a travelling wave
$y = 2\,cos\,(3x)\,sin\,(10t)$
$y = 2\,\sqrt {x - vt}$
$y = 3\,sin\,(5x -0.5t) + 4\,cos\,(5x -0.5t)$
$y = cos\,x\,sin\,t + cos\,2x\,sin\,2t$
Two identical sounds $S_1$ and $S_2$ reach at a point $P$ in phase. The resultant loudness at point $P$ is $n\,\, dB$ higher than the loudness of $S_1$. The value of $n$ is
A string with a mass density of $4\times10^{-3}\, kg/m$ is under tension of $360\, N$ and is fixed at both ends. One of its resonance frequencies is $375\, Hz$. The next higher resonance frequency is $450\, Hz$. The mass of the string 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
Two vibrating tuning forks produce progressive waves given by $Y_1 = 4\, sin\, 500\pi \,t$ and $Y_2 = 2\, sin\, 506 \pi \,t$. Number of beats produced per minute is
A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T (Y =$ young’s modulus, $\rho =$ density, $\alpha =$ coefficient of linear expansion) then the frequency of transverse vibration is proportional to :