A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length
`mu,2mu,3mu and 4mu` respectively. The instrument is played by vibrating the strings by varying the free length in between the range
`L_0 and 2L_0`. It is found that in string-1
`(mu)` at free length `L_0` and tension `T_0` the fundamental mode frequency is `f_0` .
List-I gives the above four strings while list-II lists the magnitude of some quantity.

If the tension in each string is `T_0`, the correct match for the highest fundamental frequency in `f_0` units will be -

A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length mu,2mu,3mu and 4mu respectively. The instrument is played by vibrating the strings by varying the free length in between the range L_0 and 2L_0 . It is found that in string-1 (mu) at free length L_0 and tension T_0 the fundamental mode frequency is f_0 . List-I gives the above four strings while list-II lists the magnitude of some quantity. The length of the strings 1,2,3 and 4 are kept fixed at L_0 ,(3L_0)/2,(5L_0)/4 and (7L_0)/4 , respectively . S trings 1,2,3 and 4 are vibrated at their 1^(st), 3^(rd), 5^(th) and 14^(th) harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of T^0 will be -

String-1 is connected with string-2. The mass per unit length in string-1 is mu_1 and the mass per unit length in string-2 is 4mu_1 . The tension in the strings is T. A travelling wave is coming from the left. What fraction of the energy in the incident wave goes into string-2 ?

Two thin rods of same length l but of different uniform mass per unit length mu_(1) and mu_(2) respectively are joined together. The system is ortated on smooth horizontal plane as shown in figure. The tension at the joint will be

Two thin rods of same length l but of different uniform mass per unit length mu_(1) and mu_(2) respectively are joined together. The system is ortated on smooth horizontal plane as shown in figure. The tension at the joint will be

When a stretched string of length L vibrating in a particular mode, the distance between two nodes on the string is l . The sound produced in this mode of vibration constitutes the nth overtone of the fundamental frequency of the string.

The frequency of vibration of string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.

The frequency of vibration of string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.

The frequency of vibration of string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.