Two waves $Y_1=A_1 \sin \,(\omega t -\beta_1)$ and $Y_2 = A_2 \sin \,(\omega t -\beta_2)$ superimpose to form a resultant wave whose amplitude is
$\sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\,\cos \,({\beta _1} - {\beta _2})} $
$\sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\,\sin \,({\beta _1} - {\beta _2})} $
$A_1 + A_2$
$(A_1 + A_2)$
A stretched wire of length $110\,cm$ is divided into three segments whose frequencies are in ratio $1 : 2 : 3.$ Their lengths must be
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 point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$are at distances of $2m$ and $3m$ respectively from the source. The ratio of the intensities of the waves at $P$ and $Q$ is
A train is moving towards a stationary observer. Which of the following curve best represents the frequency received by observer $f$ as a function of time ?
A pulse shown here is reflected from the rigid wall $A$ and then from free end $B.$ The shape of the string after these $2$ reflection will be