 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2011/paper-1/section-a/1/solution

I (t) = I (0) e^{- ω t / Q}

. Interpreting the stated loudness comparison as an intensity comparison,

\frac{I _{L} ( 2 )}{I _{H} ( 2 )} = 2 exp [- 2 (\frac{2 π ( 700 )}{Q _{L}} - \frac{2 π ( 6000 )}{1 0 ^{5}})] < 1.

Therefore the information gives an upper bound, not a unique value:

Q_{L} < \frac{2 π ( 700 )}{2 π ( 6000 ) /1 0 ^{5} + ln 2/2} ≃ 6.08 \times 1 0^{3} .

Equality would describe equal intensities at two seconds; the stated strict inequality allows every smaller positive

Q_{L}

consistent with the weak-damping model.

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