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. \(2\sqrt3~\text{mm}\)

 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:

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? 

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is \(20~\text{cm}\), the length of the open organ pipe is:
1. \(13.2~\text{cm}\)
2. \(8~\text{cm}\)
3. \(12.5~\text{cm}\)
4. \(16~\text{cm}\)