The two waves represented by $y_1 = a\,sin(\omega\,t)$ and $y_2 = b\, cos\, (\omega\, t)$ have a phase difference of

A wave travelling along the $x- $ axis is described by the equation $y(x, t) = 0.005\,\,cos(\alpha x\,-\,\beta t).$  If the wavelength and the time period of the wave are $0.08 \,\,m$ and $2.0\,\,s,$  respectively, then $\alpha $ and $\beta $ in appropriate units are

 Two cars $A$ and $B$ are moving in the same direction with speeds $36\,km/hr$ and $54\,km/hr$ respectively. Car $B$ is ahead of $A$. If $A$ sounds horn of frequency $1000\,Hz$ and the speed of sound in air is $340\,m/s$, the frequency of sound received by the driver of car $B$ is .................. $\mathrm{Hz}$

In the standing wave shown, particles at the positions $A$ and $B$ have a phase difference of

The length of open organ pipe is $L$ and fundamental frequency is $f$. Now it is immersed into water upto half of its length now the frequency of organ pipe will be

A wave $y = a\,\sin \,\left( {\omega t - kx} \right)$ on a string meets with another wave producing a node at $x = 0$. Then the equation of the unknown wave is