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Two waves are propagating along a taut string that coincides with the $x-$axis. The first wave has the wave function $y_1 = A cos [k(x - vt)]$ and the second has the wave function $y = A cos [k(x + vt) + \phi ]$.
The equation of the progressive wave, where $t$ is the time in second, $x$ is the distance in metre is $y=A \cos 240\left(t-\frac{x}{12}\right)$. The phase difference (in $SI$ units) between two positions $0.5 \,m$ apart is ...........
Two trains move towards each other with the same speed. The speed of sound is $340 \;m / s$. If the height of the tone of the whistle of one of them heard on the other changes $9 / 8$ times, then the speed of each train should be ........... $m/sec$
A source of frequency $\nu$ gives $5$ beats/second when sounded with a source of frequency $200 \;Hz$. The second harmonic of frequency $2\nu$ of source gives $10$ beats/second when sounded with a source of frequency $420\; Hz$. The value of $v$ is .... $Hz$
Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of $72\; km/hr$ and $36\; km/hr$. If first car blows horn of frequency $280\; Hz,$ then the frequency of horn heard by the driver of second car when line joining the cars make $45^o$ angle with the roads; will be .... $Hz$