question_answer

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is                                                                                                                                                      [AIEEE 2006]

A)  105 Hz     

B)       1.05 Hz

C)  1050 Hz          

D)  10.5 Hz

Correct Answer: A

Solution :

[a] For string fixed at both the ends, resonant frequency are given bywhere symbols have their usual meanings, if is given that 315 Hz and 420 Hz   are two consecutive resonant frequencies, Jet these be nth and harmonics.

...(i)

...(ii)

Dividing Eq. (i) by Eq. (ii). we get

From Eq. (i), lowest resonant frequency,