A transverse displacement of vibrating string is $y=0.06 \sin \left(\frac{2 \pi}{3}\right) \times \cos (120 \pi t)$.

If the mass per unit length of a string is $4 \times 10^{-2} \mathrm{~kg} / \mathrm{m}$, then the tension in the string will be

The equation of a progressive wave is $\mathrm{Y}=3 \sin \left[\pi\left(\frac{\mathrm{t}}{3}-\frac{\mathrm{x}}{5}\right)+\frac{\pi}{4}\right]$ where x and y are in meter and time in second. Which of the following is correct?

A vehicle starts from rest and accelerates along straight path at $2 \mathrm{~m} / \mathrm{s}^2$. At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at $94 \%$ of its value when the vehicle was at rest?

(speed of sound $=220 \mathrm{~m} / \mathrm{s}$ )

A pipe open at both ends of length 1.5 m is dipped in water at one end such that $2^{\text {nd }}$ overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz . The length of the pipe immersed in water is (Speed of sound in air $=330 \mathrm{~m} / \mathrm{s}$ ) (Neglect end correction)