The earth has a radius of $6400 \mathrm{km}$. The inner core of$1000 \mathrm{km}$radius is solid. Outside it, there is a region from$1000 \mathrm{km}$ to a radius of $3500 \mathrm{km}$ which is in the molten state. Then again from $3500 \mathrm{km}$ to $6400 \mathrm{km}$ the earth is solid. Only longitudinal $\left(P\right)$ waves can travel inside a liquid. Assume that the $P$ wave has a speed of $8 \mathrm{km}/s$ in solid parts and of $5 \mathrm{km}/s$ in liquid parts of the earth. An earthquake occurs someplace close to the surface of the earth. Calculate the time after which it will be recorded in a seismometer at a diametrically opposite point on the earth if wave travels along diameter.

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.

(a) $y=5\cos \left(4x\right)\sin 20t$

Determine the type of wave.

Given below is a function of $x$ and $t$ to represent the displacement of an elastic wave.

 $y=4\sin \left(5x-\frac{t}{2}\right)+3\cos \left(5x-\frac{t}{2}\right)$

State which of the following conditions represent the given equation.
(a) a travelling wave along –x direction

(b) a stationary wave

(c) beats

(d) a travelling wave along +x direction

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.

$y=10 \cos \left[\right(252-250\left)\pi t\right] \cos \left[\right(252+250\left)\pi t\right]$

State which of the following conditions represent the given equation.
(a) a travelling wave along –x direction

(b) a stationary wave

(c) beats

(d) a travelling wave along +x direction

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.

 $y=100\cos (100\pi t+0.5x)$

State which of the following conditions represent the given equation.
(a) a travelling wave along –x direction

(b) a stationary wave

(c) beats

(d) a travelling wave along +x direction

In the given progressive wave $y=5\sin (100\pi t-0.4\pi x)$ where $x, y$ are in $m,$ and $t$ is in seconds, What is the amplitude?

In the given progressive wave $y=5\sin (100\pi t-0.4\pi x)$ where $x, y$ are in $m,$ and $t$ is in seconds, What is the 

(b) wave length

In the given progressive wave $y=5\sin (100\pi t-0.4\pi x)$ where $x, y$ are in $m,$ and $t$ is in seconds, What is the

(c) frequency