An organ pipe $P_1$ closed at one end vibrating in its first overtone. Another pipe $P_2$  open at both ends is vibrating in its third overtone. They are in a resonance with a  given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

Four sources of sound each of sound level $10\,dB$ are sounded together, there sultant intensity level will be ... $dB$

For waves propagating in a medium, identify the property that is independent of the others

When a wave travels in a medium, the particle displacement is given by : $y = a\,\sin \,2\pi \left( {bt - cx} \right)$ where $a, b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda _2$ . The ratio $\lambda _2/\lambda _1$ is

Two monoatomic ideal gases $1$ and $2$ of molecular masses $M_1$ and $M_2$ respectively are enclosed in separate containers kept a the same temperature. The ratio of the speed of sound in gas $1$ to that in gas $2$ is