When the tension in string is increased by 3 ~kg t , the frequency of the fundamental mode increases in the ratio 2: 3 . The initial tension in the string is

Step-by-step solution

The formula for frequency is f = 1 2 l ~T ~m After increasing the tension, the frequency becomes f ^ = 1 2 l ~T +3 ~m array ll & f f ^ = T ~T +3 & 2 3 = T ~T +3 4 9 = T ~T +3 4 ~T +12=9 ~T & 5 ~T =12 & ~T =2.4 ~kg t array