The ratio of densities of nitrogen and oxygen is $14:16.$ The temperature at which the speed of sound in nitrogen will be same at that in oxygen at $55^oC$ is ..... $^oC$
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A wire of $10^{-2} kgm^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^o$ with the horizontal. Masses $m$ and $M$ are tied at two ends of wire such that m rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 ms^{^{-1}}$.
The ends of stretched wire of length $L$ are fixed at $x\, = 0$ and $x \,= L$. In one experiment, the displacement of the wire is ${y_1} = A\sin\, \left( {\pi x/L} \right)\sin \,\omega t$ and energy is $E_1$. and in another experiment its displacement is ${y_2} = A\sin \,\left( {2\pi x/L} \right)\sin 2\omega t$ and energy is $E_2$, Then
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
The length of the wire shown in figure between the pulleys is $1.5\, m$ and its mass is $12.0\,g$. The frequency of vibration with which the wire vibrates in three loops forming antinode at the mid point of the wire is $(g = 9.8 \,m/s^2)$
A source of sound of frequency $500 Hz$ is moving towards an observer with velocity $30 m/s$. The speed of sound is $330 m/s$. the frequency heard by the observer will be .... $Hz$
A metal wire of linear mass density of $9.8\, g/m$ is stretched with a tension of $10 kg$ weight between two rigid supports $1$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $n.$ The frequency $n$ of the alternating source is ..... $Hz$