Two waves represented by ${y_1} = a\sin \frac{{2\pi}}{\lambda }\left( {vt - x} \right)$ and ${y_2} = a\cos \frac{{2\pi }}{\lambda }\left( {vt - x} \right)$ are superposed. The resultant wave has an amplitude equal to
Zero
$2a$
$a$
$a\sqrt 2 $
A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v$ is the velocity of sound, the velocity of the car will be
Two pipes are each $50\,cm$ in length. One of them is closed at one end while the other is both ends. The speed of sound in air is $340\,ms^{-1}.$ The frequency at which both the pipes can resonate is
A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9\ meters$ and $25\ meters$ respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is
A wave travelling along the $x-$ axis is described by the equation $y \,(x, t ) = 0.005\, cos \,\left( {\alpha x - \beta t} \right)$. If the wavelength and the time period of the wave are $0.08\,m$ and $2.0\, s$ respectively then $a$ and $b$ in appropriate units are
Two identical flutes produce fundamental notes of frequency $300\,Hz$ at $27\,^oC$. If the temperature of air in one flute is increased to $31\,^oC$, the number of the beats heard per second will be