A musical instrument 'P' produce 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. If the amplitude of waves produced by ' P ' is ' A_P ', the amplitude of waves produced by 'Q' will be

Step-by-step solution

Energy of sound waves is proportional to the square of amplitude and the square of frequency: E A^2 n^2 . For instrument P: A_P = A , n_P = n , so E_P = kA^2 n^2 . For instrument Q: n_Q = n 4 , so E_Q = kA_Q^2 ( n 4 )^2 = kA_Q^2 n^2 16 . Given E_P = E_Q , we have: kA^2 n^2 = kA_Q^2 n^2 16 Canceling k and n^2 (for n 0 ): A^2 = A_Q^2 1 16 Solving for A_Q : A_Q^2 = 16A^2 A_Q = 4A = 4A_P The amplitude of waves from Q is four times that of P, corresponding to option B .