How many degrees of longitude are there in total around the Earth?

Plot the displacement $\left(y\right)$ versus $\left(t\right)$ graphs for $x=0,2$ and $4\mathrm{cm}$. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase?

A plane progressive wave is given by y=2cos 6.284 (30t-x). What is period of the wave?

A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is $1.7 \mathrm{km} {\mathrm{s}}^{-1}$? The operating frequency of the scanner is $4.2 \mathrm{M} \mathrm{Hz}$.

One end of a long string of linear mass density $8.0\times {10}^{-3}kg{m}^{-1}$ is connected to an electrically driven tuning fork of frequency $256 \mathrm{Hz}$. The other end passes over a pulley and is tied to a pan containing a mass of $90 \mathrm{kg}$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t=0$, the left end (fork end) of the string $x=0$ has zero transverse displacement $(y=0)$ and is moving along positive $y$-direction. The amplitude of the wave is $5.0 \mathrm{cm}$. Write down the transverse displacement $y$ as function of $x$ and $t$ that describes the wave on the string.

A stone dropped from the top of a tower of height $300 \mathrm{m}$ high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is $340 {\mathrm{ms}}^{-1}$? $(g=9.8 {\mathrm{ms}}^{-2})$ 

A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium. Does the pulse have a definite (i) frequency, (ii) wavelength, (iii) speed of propagation? 

A travelling harmonic wave on a string is described by $y(x,t)=7.5\sin \left(0.0050x+12t+\frac{\pi }{4}\right)$. What are the displacement and velocity of oscillation of a point at $x=1 \mathrm{cm}$, and $t=1 \mathrm{s}$? Is this velocity equal to the velocity of wave propagation? ($x$ is in $\mathrm{cm}$, $t$ is in $\mathrm{s}$, $\sin (12.79 \mathrm{rad})=0.2217$ and $\cos (12.79 \mathrm{rad})=0.975$) 

Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse ($S$) and longitudinal ($P$) sound waves. Typically the speed of $S$ wave is about $4.0 {\mathrm{kms}}^{-1}$, and that of $P$ wave is $8.0 {\mathrm{kms}}^{-1}$. A seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4 \min$ before the first $S$ wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?

Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?