| 1. | \(1:2\) | 2. | \(1:1\) |
| 3. | \(\sqrt{2}:1\) | 4. | \(1:\sqrt{2}\) |
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 \(\frac{\lambda_2}{\lambda_1}\) is:
| 1. | \(\sqrt{\dfrac{m_1+m_2}{m_2}}\) | 2. | \(\sqrt{\dfrac{m_2}{m_1}}\) |
| 3. | \(\sqrt{\dfrac{m_1+m_2}{m_1}}\) | 4. | \(\sqrt{\dfrac{m_1}{m_2}}\) |
A steel wire has a length of \(12.0~\text m\) and a mass of \(2.10~\text{kg}.\) 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 \(343~\text{m/s}\) )?
1. \(4.3\times10^3~\text{N}\)
2. \(3.2\times10^4~\text{N}\)
3. \(2.06\times10^4~\text{N}\)
4. \(1.2\times10^4~\text{N}\)
| 1. | \(4.0~\text{N}\) | 2. | \(12.5~\text{N}\) |
| 3. | \(0.5~\text{N}\) | 4. | \(6.25~\text{N}\) |

| 1. | maximum at \(A,\) minimum at \(O\) |
| 2. | minimum at \(A,\) maximum at \(O\) |
| 3. | uniform |
| 4. | minimum at \(A\) and \(O,\) maximum in the middle |