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})} $
$A_1 + A_2$
$(A_1 + A_2)$
Two open organ pipes of fundamental frequencies $n_1$ and $n_2$ are joined in series. The fundamental frequency of the new pipe so obtained will be
For a certain organ pipe three successive resonance frequencies are observed at $425\, Hz,595 \,Hz$ and $765 \,Hz$ respectively. If the speed of sound in air is $340 \,m/s$, then the length of the pipe is ..... $m$
In the standing wave shown, particles at the positions $A$ and $B$ have a phase difference of
Two waves represented by, $y_1 = 10\,sin\, 200\pi t$ , ${y_2} = 20\,\sin \,\left( {2000\pi t + \frac{\pi }{2}} \right)$ are superimposed at any point at a particular instant. The amplitude of the resultant wave is
If $L_1$ and $L_2$ are the lengths of the first and second resonating air columns in a resonance tube, then the wavelength of the note produced is