A taut string of length \(2\) m is fixed at both ends and plucked. The speed of waves on the string is \(3\times10^4\) m/s (see figure).

If the wavelength of the fundamental frequency is \(\lambda_1,\)​ and the wavelength of the second harmonic is \(\lambda_2,\) what is the ratio \(\dfrac{\lambda_1}{\lambda_2}?\)

A wire of length \(2L\) is formed by joining two wires, \(A\) and \(B,\) each of the same length but with different radii, \(r\) and \(2r,\) respectively, and made of the same material. The wire vibrates at a frequency such that the joint between the two wires forms a node. If the number of antinodes in wire \(A\) is \(p\) and in wire \(B\) is \(q,\) the ratio \(p:q\) is: