Equation of a Progressive Wave

Explain the destructive interference and also its condition?

When two waves are in same phase then the resultant wave_____ is equal.

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)

The two given waves are described by the following equations: $y\left(x,t\right)=\left(0.025 \mathrm{cm}\right) \sin \left[(3.14 {\mathrm{cm}}^{-1})\mathrm{x}-(157 {\mathrm{s}}^{-1})\mathrm{t}\right]$ and $y\left(x,t\right)=\left(0.025 \mathrm{cm}\right) \sin \left[(1.57 {\mathrm{cm}}^{-1})x-\left(314 {\mathrm{s}}^{-1}\right)t\right]$ are in phase.

A wave traveling along a string is described by:

$y(x,t)=3.0 \sin (3.14x-314t)$ 

All the numerical constants in the given equation are in the SI unit. Find the wavelength of a wave that is in phase with the given wave. 

Two plane-progressive waves in the same phase must have:

opposite phase for two progressive waves is generalised as $∆\mathrm{\varphi }=\left(2\mathrm{n}\pm 1\right)\mathrm{\pi }$ then what will be corresponding path difference.

Which of the followings is not correct for the two progressive waves in opposite phase.

Two progressive wave are said to be in opposite phase or out of phase if phase difference becomes ${180}^{\mathrm{o}}=\mathrm{\pi }$

When two progressive waves ${\mathrm{y}}_1=6 \sin \left(2\mathrm{x}-8\mathrm{t}\right)$ and ${\mathrm{y}}_2=8 \sin \left(2\mathrm{x}-8\mathrm{t}-\mathrm{\pi }\right)$ are super imposed. The amplitude of resultant wave is (in $\mathrm{cm}$).

Angular wave number is also called as propagation constant or wave vector K.

What is wave number in terms of wavelength?

What is the relation between angular frequency and the time period of a wave?

Two sinusoidal waves with same wavelengths and amplitudes travel in opposite directions along a string with a speed $10 {\mathrm{ms}}^{-1}.$ If the minimum time interval between two instants when the string is flat is $0.5 \mathrm{s},$ the wavelength of the waves is