A muscial 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. If the amplitude of waves produced by p is `A_(P)`, then the amplitude of waves produced by Q will be

Options

A. `2A_(P)`
B. `4A_(P)`
C. `6A_(P)`
D. `9A_(P)`

Answer

B

Explanation

The energy of the wave
= The energy of the harmonic oscillator
`= (1)/(2) m omega^(2) A^(2) = (1)/(2) m. (2pi n)^(2) A^(2) = 2pi^(2) n^(2) A^(2) m`
`:. E prop n^(2) A^(2)`
But `E_(P) = E_(Q)`
`:. n_(P)^(2) A_(P)^(2) = n_(q)^(2) A_(Q)^(2)`
`:. ((A_(Q))/(A_(P)))^(2) = ((n_(P))/(n_(Q)))^(2)`
`:. (A_(Q))/(A_(P)) = (n_(P))/(n_(Q)) = (n)/(n//4) = 4`
`:. A_(Q) = 4A_(P)`