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Two Waves of the Same Pitch Have Their Amplitudes in the Ratio 2 : 3. (I) What Will Be the Ratio of Their Loudness? (Ii) What Will Be the Ratio of Their Frequencies?

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प्रश्न

Two waves of the same pitch have their amplitudes in the ratio 2 : 3.
(i) What will be the ratio of their loudness?
(ii) What will be the ratio of their frequencies?

संख्यात्मक
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उत्तर

(i) Given, the Amplitude ratio, a1 : a2 = 2 : 3

∵ I α a2

∴ `"I"_1/"I"_2="a"_1^2/"a"_2^2=2^2/3^2=4/9`

⇒ I1 : I2 = 4 : 9

(ii) ∵ Frequency α Pitch

∴ Ratio of frequencies = 1 : 1

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