In each of the four situations of column-I , a stretched string or an organ pipe is given along with the required data. In case of strings the tension in string is T=102.4 N and the mass per unit length of string is 1g/m. Speed of sound in air is 320 m/s. Neglect end corrections.The frequencies of resonance are given in column-II.Match each situation in column-I with the possible resonance frequencies given in Column-II.

Options

A. `{:(,p,q,r,s),((A),1,3,2,4):}`
B. `{:(,p,q,r,s),((B),1,4,3,2):}`
C. `{:(,p,q,r,s),((C ),3,2,4,1):}`
D. `{:(,p,q,r,s),((D ),2,4,1,3):}`

Explanation

(A) The fundamental frequency in the string.
`f_0=sqrt(T//mu)/(2l)=sqrt(102.4/(1xx10^-3))xx1/(2xx0.5)Hz=320 Hz`.
Other possible resonance frequencies are `f_A and f_0=320 Hz, 640 Hz, 960 Hz`
(B)The fundamental frequency in the string.
`f_0=sqrt(T//mu)/(4l)=320/(4xx0.5)=160 Hz`.
Other possible resonance frequencies are
`f_B`=160 Hz, 480 Hz, 800 Hz.
(C )The fundamental frequency in both ends open organ pipe is
`f_0=v/(2l)=320/(2xx0.5)=320 Hz`
Other possible resonance frequencies are
`f_c=320 Hz,640 Hz, 960 Hz`
(D)The fundamental frequency in one end open organ pipe is
`f_0=v/(4l)=320/(4xx0.5)=160 Hz`
Other possible resonance frequencies are `f_D=160 Hz, 480 Hz, 800 Hz`