A sound of frequency $$480 \mathrm{~Hz}$$ is emitted from the stringed instrument. The velocity of sound in air is $$320 \mathrm{~m} / \mathrm{s}$$. After completing 180 vibrations, the distance covered by a wave is

A sonometer wire '$$A$$' of diameter '$$\mathrm{d}$$' under tension '$$T$$' having density '$$\rho_1$$' vibrates with fundamental frequency '$$n$$'. If we use another wire '$$B$$' which vibrates with same frequency under tension '$$2 \mathrm{~T}$$' and diameter '$$2 \mathrm{D}$$' then density '$$\rho_2$$' of wire '$$B$$' will be

The upper end of the spring is fixed and a mass '$$m$$' is attached to its lower end. When mass is slightly pulled down and released, it oscillates with time period 3 second. If mass '$$\mathrm{m}$$' is increased by $$1 \mathrm{~kg}$$, the time period becomes 5 second. The value of '$$\mathrm{m}$$' is (mass of spring is negligible)

What should be the diameter of a soap bubble, in order that the excess pressure inside it is $$25.6 \mathrm{~Nm}^{-2}$$ ? [surface tension of soap solution $$\left.=3 \cdot 2 \times 10^{-2} \mathrm{~Nm}^{-2}\right]$$