A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

In an open organ pipe $\nu_3$ and $\nu_6$ are $3^{\text {rd }}$ and $6^{\text {th }}$ harmonic frequencies, respectively. If $\nu_6-\nu_3=2200 \mathrm{~Hz}$ then length of the pipe is $\_\_\_\_$ mm .

(Take velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$.)

Two strings $(A, B)$ having linear densities $\mu_A=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and, $\mu_B=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and lengths $L_A=2.5 \mathrm{~m}$ and $L_B=1.5 \mathrm{~m}$ respectively are joined. Free ends of $A$ and $B$ are tied to two rigid supports $C$ and $D$, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from $C$ and $D$ ends, take time $t_1$ and $t_2$, respectively, to reach the joint. The ratio $t_1 / t_2$ is:

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_1(x, t) = 4 \sin (kx - \omega t)$ and $y_2(x, t) = 2 \sin (kx - \omega t + \frac{2\pi}{3})$, are:

(Take the angular frequency of initial waves same as $\omega$)