As shown in figure string $PQR$ is stretched by force $F=(3-10kt) \mathrm{N},$ where $k$ is a constant and $t$ is time in second. At time $t=0,$ a pulse is generated at the end $P$ of the string. Find the value of $k$ $\left(\mathrm{in} \mathrm{N} {\mathrm{s}}^{-1}\right),$ if the value of force become zero as the pulse reaches at point $Q.$ (Assume linear mass density is constant and having value $0.3 \mathrm{g} {\mathrm{cm}}^{-1})$

The phase difference between the following two waves $y_2$ and $y_1$ is:

$y_1=a\sin \left(\omega t-kx\right)$

$y_2=b\cos \left(\omega t-kx+\frac{\pi }{3}\right)$

Two simple harmonic motion, are represented by the equations $y_1=10\sin \left(3\pi t+\frac{\pi }{3}\right); y_2=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)$. Ratio of amplitude of $y_1$ to $y_2=x:1$. The value of $x$ is

A simple wave motion is represented by $y=5\left(\sin 4\pi t+\sqrt{3}\cos 4\pi t\right)$. Its amplitude is

The figure below shows pressure variation in two different sound waves in air with time at a given position. Both the figures are drawn to the same scale.



Which of the following statement is true?