Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of $6\, beats/s$ when both the wires oscillate together would be

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 ..... $Hz$

In a Fraunhofer's diffraction obtained by a single slit aperture, the value of path difference for $n^{th}$ order of minima is

Equation of a plane progressive wave is given by $y = 0.6\, \sin 2\pi \left( {t - \frac{x}{2}} \right)$.On reflection from a denser medium its amplitude becomes $2/3$ of the amplitude of the  incident wave. The equation of the reflected wave is :-

A car blowing a horn of frequency $350\, Hz$ is moving normally towards a wall with a  speed of $5 \,m/s$. The beat frequency heard by a person standing between the car and  the wall is ..... $Hz$ (speed of sound in air $= 350\, m/s$)

A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2/\lambda _1$ is