In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz . When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz . The value of m is ______ g .

Step-by-step solution

The formula to calculate the fundamental frequency in a stretched string is given by f = 1 2 L T μ       . . . 1 For the first mass, it can be written that f 1 = 1 2 L m 1 g μ       . . . 2 And, for the second mass, it can be written that f 2 = 1 2 L m 2 g μ       . . . 3 Divide equation (3) by equation (2) and simplify to obtain the required mass. f 2 f 1 = 1 2 L m 2 g μ 1 2 L m 1 g μ =   m 2 m 1 ⇒ m 1 m 2 = f 1 f 2 2 ⇒ m 2 = m