A string has mass per unit length of $10^{-6} \mathrm{~kg} / \mathrm{cm}$ The equation of simple harmonic wave produced in it is $\mathrm{Y}=0.2 \sin (2 \mathrm{x}+80 \mathrm{t}) \mathrm{m}$. The tension in the string is

The driver of a car travelling with a speed ' $V_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall sounds a siren of frequency ' $n$ ' Hz. If the velocity of sound in air is $\mathrm{V} \mathrm{m} / \mathrm{s}$, then the frequency of sound reflected from the wall and as heard by the driver, in Hz , is

An open organ pipe of length ' $l$ ' is sounded together with another open organ pipe of length $\left(l+l_1\right)$ in their fundamental modes. Speed of sound in air is ' $V$ '. The beat frequency heard will be ( $\left.l_1< < l\right)$

Two progressive waves $Y_1=\sin 2 \pi\left(\frac{t}{0 \cdot 4}-\frac{x}{4}\right)$ and $Y_2=\sin 2 \pi\left(\frac{t}{0 \cdot 4}+\frac{x}{4}\right)$ superpose to form a standing wave. ' $x$ ' and ' $y$ ' are in SI system. Amplitude of the particle at $x=0.5 \mathrm{~m}$ is $\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]$