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**Unformatted text preview: **15.61: a) μF = F μ F = F v = F k ω and substituting this into Eq. (15.33) gives the result. b) Quadrupling the tension for F to F ′ = 4 F increases the speed v = F μ by a factor of 2, so the new frequency ω′ and new wave number k ′ are related to ω and k by (ω′ k ′) = 2(ω k ). For the average power to be the same, we must have Fkω = F ′k ′ω′, so kω = 4k ′ω′ and k ′ω′ = kω 4 . Multiplying the first and second equations together gives ω′2 = ω 2 2, so ω′ = ω 2. 2. Dividing the second equation by Thus, the frequency must decrease by a factor of the first equation gives k ′2 = k 2 8, so k ′ = k 8. ...

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