A musical instrument P produces sound waves of frequency 'n' and amplitude 'A'. Another musical instrument Q produces sound waves of frequency n/4. The waves produced by P and Q have equal energies. The amplitude of waves produced by Q will be

Step-by-step solution

The energy of a sound wave is directly proportional to the square of its frequency and the square of its amplitude. E f^2 A^2 Given that the waves produced by P and Q have equal energies: E_P = E_Q f_P^2 A_P^2 = f_Q^2 A_Q^2 Substituting the given values f_P = n , A_P = A , and f_Q = n 4 : n^2 A^2 = ( n 4 )^2 A_Q^2 n^2 A^2 = n^2 16 A_Q^2 A_Q^2 = 16 A^2 A_Q = 4A Answer: 4A