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

Two waves of sound having intensities $I$ and $4I$ interfere to produce interference pattern. The phase difference between the waves is $\pi /2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is

A transverse wave is described by the equation $y = {y_0}\sin 2\pi \left( {ft - \frac{x}{\lambda }} \right)$. The maximum particle velocity is equal to four times wave velocity if

A string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of transverse wave along the string at a distance $'x'$ from the free end will be

A car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. Speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is   .... $Hz$

When two sound sources of the same amplitude but of slightly different frequencies $v_1$ and $v_2$ are sounded simultaneously, the sound one hears has a frequency equal to