The frequency of the whistle of a train moving with a constant speed is observed by a stationary detector on the platform to be $v_1$. The frequency of the same whistle is detected to be $v_2$ inside another train moving on a parallel track, at a speed $v$ towards the frst train. If the speed of sound in air is taken to be $v_s$ ound, what is the ratio $v / v_s$ ound?

A uniform taut string with two point charges $q$ and $-q$ attached to its ends passes over two massless pullies kept $L$ distance apart as shown in the fgure. If $f$ is the fundamental frequency of the part of the string over pullies, which of the following statements is correct?