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A uniform metal wire of density $\rho $, cross-sectional area $A$ and length $L$ is stretched with a tension $T$. The speed of transverse wave in the wire is given by
A closed organ pipe $150 \mathrm{~cm}$ long gives $7$ beats per second with an open organ pipe of length $350 \mathrm{~cm}$, both vibrating in fundamental mode. The velocity of sound is_________ $\mathrm{m} / \mathrm{s}$.
A string is stretched between fixed points separated by $75.0\,\, cm.$ It is observed to have resonant frequencies of $420\,\, Hz$ and $315\,\, Hz$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is .... $Hz$
Two wires are in unison. If the tension in one of the wires is increased by $2\%, 5$ beats are produced per second. The initial frequency of each wire is .... $Hz$
A transverse wave of frequency $500 \,Hz$ and speed $100 \,m / s$ is travelling in the positive $x$-direction on a long string. At time $t=0 \,s$, the displacements at $x=0.0 \,m$ and at $x=0.25 \,m$ are $0.0 \,m$ and $0.02 \,m$, respectively. The displacement at $x=0.2 \,m$ at $t=5 \times 10^{-4} s$ is ............ $m$
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 .... $ cm$
A narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at the positions right angle to each other. A source placed at $S$ generated a wave of intensity $I_0$ which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point $D$ where a detector is placed The maximum intensity produced at $D$ is given by
Statement$-1:$ Two longitudinal waves given by equations $y _{1}( x , t )=2 a \sin (\omega t - kx )$ and $y _{2}( x , t )= a \sin (2 \omega t -2 kx )$ will have equal intensity.
Statement$-2:$ Intensity of waves of given frequency in same medium is proportional to square of amplitude only.