$A$ stone thrown into still water creates a circular wave pattern moving radially outwards. If $r$ is the distance measured from the centre of the pattern, the amplitude of the wave varies as

The amplitude of a wave at a distance $r$ from a point source is $A$. What will be the amplitude at a distance $2r$ from the source?

The relation between time and displacement for two particles is given by
${y_1} = 0.06 \sin 2\pi (1.04t + {\phi _1})$
${y_2} = 0.03 \sin 2\pi (1.04t + {\phi _2})$
The ratio of the intensity of the waves produced by the vibrations of the two particles will be

$A$ transverse wave is passing through a stretched string with a speed of $20 \ m/s$. The tension in the string is $20 \ N$. At a certain point $P$ on the string,it is observed that energy is being transferred at a rate of $40 \ mW$ at a given instant. Find the speed of point $P$.

$A$ travelling wave is partly reflected and partly transmitted from a rigid boundary. Let $a_i, a_r$ and $a_t$ be the amplitudes of the incident wave,reflected wave,and transmitted wave,and $I_i, I_r$ and $I_t$ be the corresponding intensities. Choose the correct alternative.

The intensity level at a distance of $200 \ cm$ from a sound source is $80 \ dB$. If there is no loss of acoustic power in the air and the threshold intensity of hearing is $10^{-12} \ W/m^2$,what is the intensity level at a distance of $400 \ cm$ from the source (in $dB$)?