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

A car sounding its horn at $480\,Hz$ moves towards a high wall at a speed of $20\,m/s$. If the speed of sound is $340\,m/s,$ the frequency of the reflected sound heard by the passenger sitting in the car will be the nearest to ..... $Hz$

A string fixed at one end is vibrating in its second overtone. The length of the string is $10\  cm$ and maximum amplitude of vibration of particles of the string is $2\ mm$ . Then the amplitude of the particle at $9\ cm$ from the open end is

When a wave travels in a medium, the particle displacement is given by : $y = asin\, 2 \pi \,(bt -cx)$, where $a, b$ and $c$ are constants. The maximum particle velocity will  be twice the wave velocity if

A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T (Y =$ young’s modulus, $\rho =$ density, $\alpha =$ coefficient of linear expansion) then the frequency of transverse vibration is proportional to : 

A set of $24$ tunning fork is arranged in a series of increasing frequencies. If each fork gives $4\, beats/second$ with the preceeding one and frequency of last tunning fork is two times of first fork. Find frequency of $5^{th}$ tunning fork  .... $Hz$