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

Subtopic:  Beats |
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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 

Subtopic:  Standing Waves |
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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

Subtopic:  Standing Waves |
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If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is : 
1. 1:2
2. 1:1
3. \(\sqrt{2}:1\)
4. \(1:\sqrt{2}\)
Subtopic:  Travelling Wave on String |
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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.  \(2\sqrt3~\text{mm}\)

Subtopic:  Standing Waves |
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An organ pipe filled with a gas at 27°C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90°C, the resonance frequency at the same mode will be:
1.  420 Hz
2.  440 Hz
3.  484 Hz
4.  512 Hz
Subtopic:  Standing Waves |
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