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

A train is moving towards a stationary observer. Which of the following curve best represents the frequency received by observer $f$ as a function of time ?

Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $f_1$ and the other with frequency $f_2$. The ratio $\frac{f_1}{f_2}$ is given by

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

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

A pulse shown here is reflected from the rigid wall $A$ and then from free end $B.$ The shape of the string after these $2$ reflection will be