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AP EAMCET20228 Jul 2022Evening ShiftPhysicsWaves and SoundActual

Two wires A and B of lengths in the ratio 1: 2 and masses in the ratio 2: 1 are stretched by same tension. The ratio of the fundamental frequencies of wires A and B is

Options

  1. A2 2 : 1
  2. B1: 2
  3. C1: 1
  4. D2 : 1

Correct answer

C. 1: 1

Step-by-step solution

Fundamental frequency in a stretched wire is given as, f= 1 2 L T Ratio of fundamental frequencies of wire A and B , aligned f_A f_B & = 1 2 L_A T_A _A 2 L_B T _B T_B & = L_B L_A T_A T_B _B _A aligned Here L_B L_A = 2 1 aligned _A _B = m_A / L_A m_B / L_B = m_A m_B L_B L_A = 2 1 2 1 & & [ m_A m_B = 2 1 and L_B L_A = 2 1 ] aligned or _A _B = 2 1 2 1 = 4 1 _B _A = 1 4 So, f_A f_B = 2 1 1 1 4 =1: 1

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