A pendulum clock is running fast. To correct its time, we should

A pipe closed at one end has length $$0.8 \mathrm{~m}$$. At its open end $$0.5 \mathrm{~m}$$ long uniform string is vibrating in its $$2^{\text {nd }}$$ harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $$50 \mathrm{~N}$$ and the speed of sound is $$320 \mathrm{~m} / \mathrm{s}$$, the mass of the string is

Two coherent sources 'P' and 'Q' produce interference at point 'A' on the screen, where there is a dark band which is formed between 4^th and 5^th bright band. Wavelength of light used is 6000 $$\mathop A\limits^o $$. The path difference PA and QA is

The equation of simple harmonic wave produced in the string under tension $$0.4 \mathrm{~N}$$ is given by $$\mathrm{y=4 \sin (3 x+60 t) ~m}$$. The mass per unit length of the string is