The displacement of an elastic wave is given by the function : $y = 3\, sin\,\omega t + 4\, cos\,\omega t$ where $y$ is in $cm$ and $t$ is in $s$. The resultant amplitude is ...... $cm$

The diagram shows snapshot of a wave at time $t = 0$. The particle at $x = x_1$ is moving upward at that instant. Direction of propagation of wave is

An organ pipe $P_1$ closed at one end vibrating in its first overtone. Another pipe $P_2$  open at both ends is vibrating in its third overtone. They are in a resonance with a  given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v$ is the velocity of sound, the velocity of the car will be

$56$ tuning forks are so arranged in increasing order of frequencies in series that each fork gives $4$ beats per second with the previous one. The frequency of the last fork is the octave of the first. The frequency of the first fork is ..... $Hz$

When a wave travels in a medium, the particle displacement is given by : $y = asin\, 2 \pi \,(bt -cx)$, where $a, b$ and $c$ are constants. The maximum particle velocity will  be twice the wave velocity if