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 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz.  If the frequency of A is 530 Hz, the original frequency of B will be

1. 524 Hz

 2. 536 Hz

3. 537 Hz

 4.523 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 

A tuning fork with a frequency of 800 Hz produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths of 9.75 cm, 31.25 cm, and 52.75 cm. The speed of the sound in air is:

1. 500 m/s

2. 156 m/s

3. 344 m/s

4. 172 m/s

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C , two successive resonances are produced at 20 cm and 73 cm column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is:

1. 330 m/s

2. 339 m/s

3. 350 m/s

4. 300 m/s

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 cm, the length of the open organ pipe is:

1. 13.2 cm

2. 8 cm

3. 12.5 cm

4. 16 cm