| 1. | \(3:1\) | 2. | \(1:2\) |
| 3. | \(2:1\) | 4. | \(1:3\) |
| 1. | \(8:9\) | 2. | \(9:7\) |
| 3. | \(9:8\) | 4. | \(7:9\) |
| 1. | \(1:2\) | 2. | \(1:1\) |
| 3. | \(\sqrt{2}:1\) | 4. | \(1:\sqrt{2}\) |
A string of length \(l\) is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is \(2\) mm. The amplitude of a particle at a distance \(l/8\) from the fixed end is:
| 1. | \(2\sqrt2~\text{mm}\) | 2. | \(4~\text{mm}\) |
| 3. | \(\sqrt2~\text{mm}\) | 4. | \(2\sqrt3~\text{mm}\) |
| 1. | \(420~\text{Hz}\) | 2. | \(440~\text{Hz}\) |
| 3. | \(484~\text{Hz}\) | 4. | \(512~\text{Hz}\) |
In a guitar, two strings \(A\) and \(B\) made of same material are slightly out of tune and produce beats of frequency \(6~\text{Hz}\). When tension in \(B\) is slightly decreased, the beat frequency increases to \(7~\text{Hz}\). If the frequency of \(A\) is \(530~\text{Hz}\), the original frequency of \(B\) will be:
| 1. | \(524~\text{Hz}\) | 2. | \(536~\text{Hz}\) |
| 3. | \(537~\text{Hz}\) | 4. | \(523~\text{Hz}\) |
The length of the string of a musical instrument is \(90\) cm and has a fundamental frequency of \(120\) Hz. Where should it be pressed to produce a fundamental frequency of \(180\) Hz?
| 1. | \(75\) cm | 2. | \(60\) cm |
| 3. | \(45\) cm | 4. | \(80\) cm |
| 1. | \(500\) m/s | 2. | \(156\) m/s |
| 3. | \(344\) m/s | 4. | \(172\) m/s |
| 1. | \(330\) m/s | 2. | \(339\) m/s |
| 3. | \(350\) m/s | 4. | \(300\) m/s |
| 1. | \(13.2~\text{cm}\) | 2. | \(8~\text{cm}\) |
| 3. | \(12.5~\text{cm}\) | 4. | \(16~\text{cm}\) |