(a) Compute the derivative of the speed of a wave on a string with respect to the tension dv/dFT and show that the differential dv and dFT obey dv/v = V2DFT/FT. (Use the following as necessary: v and FT.) dv dF (b) A wave moves with a speed of 295 m/s on a string that is under tension of 520 N. Using the differential approximation, estimate how much the tension must be changed to increase the speed to 311 m/s. AFT = (c) Calculate AFT exactly and compare it to the differential approximation result in Part (b). Assume that the string does not stretch with the increase in tension. N % difference
(a) Compute the derivative of the speed of a wave on a string with respect to the tension dv/dFT and show that the differential dv and dFT obey dv/v = V2DFT/FT. (Use the following as necessary: v and FT.) dv dF (b) A wave moves with a speed of 295 m/s on a string that is under tension of 520 N. Using the differential approximation, estimate how much the tension must be changed to increase the speed to 311 m/s. AFT = (c) Calculate AFT exactly and compare it to the differential approximation result in Part (b). Assume that the string does not stretch with the increase in tension. N % difference
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Transcribed Image Text:(a) Compute the derivative of the speed of a wave on a string with respect to the tension dv/dFT and show that the differential dv and dF obey dv/v = V2dFT/FT. (Use the
following as necessary: v and FT.)
dv
=
dF
(b) A wave moves with a speed of 295 m/s on a string that is under a tension of 520 N. Using the differential approximation, estimate how much the tension must be
changed to increase the speed to 311 m/s.
AFT =
(c) Calculate AF exactly and compare it to the differential approximation result in Part (b). Assume that the string does not stretch with the increase in tension.
N
% difference
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