A steel wire has a length of \(12.0\) m and a mass of \(2.10\) kg. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air, at \(20^{\circ}\text{C}\) (which is \(343\) m/s)?
1. \(4.3\times10^3\) N
2. \(3.2\times10^4\) N
3. \(2.06\times10^4\) N
4. \(1.2\times10^4\) N

A steel wire \(0.72~\text{m}\) long has a mass of \(5\times10^{-3}~\text{kg}\). If the wire is under tension of \(60~\text{N}\), the speed of transverse waves on the wire will be:
1. \(85~\text{m/s}\)
2. \(83~\text{m/s}\)
3. \(93~\text{m/s}\)
4. \(100~\text{m/s}\)

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 \(\lambda_2\)${\mathrm{}}_{}$. The ratio \(\frac{\lambda_2}{\lambda_1}\) is:
1. \(\sqrt{\frac{m_1+m_2}{m_2}}\)
2. \(\sqrt{\frac{m_2}{m_1}}\)
3. \(\sqrt{\frac{m_1+m_2}{m_1}}\)
4. \(\sqrt{\frac{m_1}{m_2}}\)

The graph between fundamental frequency (\(f\)) and corresponding tension (\(T\)) in a sonometer wire is best-represented by:

1.		2.
3.		4.