The equation of displacement of two waves are given as ${y_1} = 10\,\sin \,\left( {3\pi t\, + \,\pi /3\,} \right)$ , ${y_2} = 5\,\left( {\sin \,3\pi t + \,\sqrt 3 \,\cos \,3\pi t} \right)$ , then what is the ratio of their amplitude 

A sound-source is moving in a circle and an observer is outside the circle at $O$ as shown in figure. If the frequencies as heard by the listener are $\nu _1, \nu _2$ and $\nu _3$ when the source is at $A, B$ and $C$ position, respectively, then

When two sound sources of the same amplitude but of slightly different frequencies $v_1$ and $v_2$ are sounded simultaneously, the sound one hears has a frequency equal to

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

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

The ratio of the velocity of sound in hydrogen $(\gamma = 7/5)$ to that in helium $(\gamma = 5/3)$ at  the same temperature is