Sound as a Pressure Wave

Which of the following equations does not represent a progressive wave?

Equation of a longitudinal wave is given as $s={10}^{-2}\sin 2\pi \left(1000t+\frac{50x}{17}\right)$(all SI units). Find the location $x$ (in $\mathrm{m}$), at $t=0$, where the magnitude of the change in pressure is maximum.

The phase difference between displacement and particle velocity is

The phase difference between displacement and pressure wave equation of longitudinal wave.

If mean coordinate the particle of longitudinal wave be $x_m$ then minimum coordinate of displacement will be.

If mean co-ordinate of the particle of longitudinal wave be $x_m$, then what will be maximum co-ordinate of displacement ($a$ = amplitude)

A displacement versus time graph ($s$-$t$graph) is as shown for particles at $x=0$, for a sound wave which is propagating towards left. (negative $x$-axis)

If $P$ is change in pressure, then choose correct matching of the graphs.

A small speaker has a capacity of power $3 \mathrm{W}$. A microphone is placed at distance $2 \mathrm{m}$ from the speaker. Find the displacement amplitude of particles of air near the microphone. The frequency of sound emitted by the speaker is $1 \mathrm{kHz}$. (Density of air = $1.2 \mathrm{kg} {\mathrm{m}}^{-3}$ and speed of sound in air = $330 \mathrm{m} {\mathrm{s}}^{-1}$ )

If given graph represents the variation of displacement wave for sound wave in an air tube. Which will be the pressure variation for tube?

The equation of a sound wave in air is

$P=0.01\cos \left(1000t-3x\right)$

where $P$, $x$ and $t$ are in SI units. The bulk modulus of elasticity is $1.4\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$. The displacement amplitude is

The displacement $y$ of a particle in a medium can be expressed as :
$y={\mathrm{10}}^{-6}\sin \left(\mathrm{100}t-\mathrm{20}x+\pi /4\right) \mathrm{m}$, where $t$ is in second and $x$ in meter. The speed of the wave is