A transverse wave on a string is described by $y=3 \sin (36 t+0.018 x+\pi / 4)$. where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is $\_\_\_\_$ cm . (Nearest integer)

$$ (\pi=3.14) $$

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tuning fork A is _________ Hz.

The velocity of sound in air is doubled when the temperature is raised from $0^{\circ} \mathrm{C}$ to $\alpha{ }^{\circ} \mathrm{C}$. The value of $\alpha$ is $\_\_\_\_$ .

Two loudspeakers $\left(L_1\right.$ and $\left.L_2\right)$ are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$, at equidistance to both loud speakers, is moved by 25 m along the line $A B$ while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is $\_\_\_\_$ Hz (Speed of sound in air is $324 \mathrm{~m} / \mathrm{s}$ and $\sqrt{5}=2.23$ )