Two waves of amplitudes $A_0$ and $x A_0$ pass through a region. If $x > 1$,the difference between the maximum and minimum resultant amplitude possible is

Four harmonic waves of equal frequencies and equal intensities $I_0$ have phase angles $0, \pi / 3, 2 \pi / 3$ and $\pi$. When they are superposed,the intensity of the resulting wave is $nI_0$. The value of $n$ is

Two identical sinusoidal waves each of amplitude $10 \,mm$, with a phase difference of $90^{\circ}$ are travelling in the same direction in a string. The amplitude of the resultant wave is

Two sources of sound $A$ and $B$ produce waves of $350 Hz$,and they vibrate in the same phase. $A$ particle $P$ is vibrating under the influence of these two waves. If the amplitudes at point $P$ produced by the two waves are $0.3 mm$ and $0.4 mm$,what will be the resultant amplitude of the point $P$ when $AP - BP = 25 cm$ and the velocity of sound is $350 m/s$?

Two small identical speakers are connected in phase to the same source. The speakers are $3 \,m$ apart and at ear level. An observer stands at $P, 4 \,m$ in front of one speaker as shown. The sound she hears is least intense when the wavelength is $\lambda_1$ and most intense when the wavelength is $\lambda_2$. Then,the possible values of $\lambda_1$ and $\lambda_2$ are

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at point $D$ where a detector is placed. The maximum value of $\lambda$ to produce a minima at $D$ is given by