A hearing test is conducted on an aged person. It is found that her threshold of hearing is $20 \mathrm{dB}$ at $1 \mathrm{kHz}$, and it rises linearly with frequency to, $60 \mathrm{dB}$ at, $9 \mathrm{kHz}$. The minimum intensity of sound that the person can hear at, $5 \mathrm{kHz}$ is,

A transverse wave propagating on a stretched string of linear density $3\times {10}^{-4} {\mathrm{kgm}}^{-1}$ is represented by the equation

$y=0.2\sin (1.5x+60t)$

where, $x$ in metres and $t$ is in seconds. The tension in the string (in Newton) is

A uniform string of length $20 \mathrm{m}$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is 

(Take, $\mathrm{g}=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$)

A transverse wave propagating along $x$ -axis is represented by

$y\left(x,t\right)=8.0\sin \left(0.5\pi x-4\pi t-\frac{\pi }{4}\right)$

where $x$ is in meters and $t$ is in seconds. The speed of the wave is