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

A train is moving towards a stationary observer (at $t = 0$) with constant velocity of $20\ m/s$ and after sometime it crosses the observer. Which of the following curve best represents the frequency received by observer $f$ as a function of time ?

The length of open organ pipe is $L$ and fundamental frequency is $f$. Now it is immersed into water upto half of its length now the frequency of organ pipe will be

Fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is

An organ pipe $P_1$ closed at one end vibrating in its first overtone. Another pipe $P_2$  open at both ends is vibrating in its third overtone. They are in a resonance with a  given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is