A string is stretched between two fixed points separated by . It is observed to have resonant frequencies of  and . There are no other resonant frequencies between these two. The lowest resonant frequency for this string is :      

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is . The next larger length of the column resonating with the same tuning fork is :

The two nearest harmonics of a tube closed at one end and open at other end are  and . What is the fundamental frequency of the system?  

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  two successive resonances are produced at  and  of column length. If the frequency of the tuning fork is , the velocity of sound in air at  is

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 , the length of the open organ pipe is

In a guitar, two strings  and  made of same material are slightly out of tune and produce beats of frequency . When tension in B is slightly decreased, the beat frequency increases to . If the frequency of is 530 , the original frequency of  will be

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:           

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is