The intensities of two notes are equal. If frequency of one note is one-fourth that of the other then the ratio of their amplitudes is

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Solution

The correct option is B 4
$I = \frac{1}{2} μ ω^{2} A^{2}$
$ω = 2 π f$
Thus, $I \propto f^{2} A^{2}$
$\frac{I_{1}}{I_{2}} = 1 = \frac{f_{1}^{2} A_{1}^{2}}{f_{2}^{2} A_{2}^{2}}$
$f_{1}^{2} A_{1}^{2} = (1 / 4 f_{1})^{2} A_{2}^{2}$
Thus, $A_{2}^{2} = 16 A_{1}^{2}$ or $A_{2} = 4 A_{1}$

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The intensities of two notes are equal. If frequency of one note is one-fourth that of the other then the ratio of their amplitudes is

The correct option is B 4I=12μω2A2ω=2πfThus, I∝f2A2I1I2=1=f21A21f22A22f21A21=(1/4f1)2A22Thus, A22=16A21 or A2=4A1

The correct option is B 4
$I = \frac{1}{2} μ ω^{2} A^{2}$
$ω = 2 π f$
Thus, $I \propto f^{2} A^{2}$
$\frac{I_{1}}{I_{2}} = 1 = \frac{f_{1}^{2} A_{1}^{2}}{f_{2}^{2} A_{2}^{2}}$
$f_{1}^{2} A_{1}^{2} = (1 / 4 f_{1})^{2} A_{2}^{2}$
Thus, $A_{2}^{2} = 16 A_{1}^{2}$ or $A_{2} = 4 A_{1}$