A taut string for which = 5.60 10-2 kg/m is under a tension of 87.0 N. How much

Question

A taut string for which = 5.60 10-2 kg/m is under a tension of 87.0 N. How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60.0 Hz and an amplitude of 6.00 cm? SOLVE IT Conceptualize Consider this figure and notice that the vibrating blade supplies energy to the string at a certain rate. This energy then propagates to the right along the string Categorize We evaluate quantities from equations developed in the chapter, so we categorize this example as a substitution problem Use the power of a wave equation to evaluate the power: 1.242 2 substitute for and v: Substitute numerical values: 2(60.0 Hz)2(0.0600 m)2V(0.056 kg/m)(87.0 N) MASTER IT HINTS What if we use another string with linear mass density 2.70 x 10-2 kg/m while keeping the same tension on the string, the same power supply and the same frequency? What will be the amplitude (in cm) of the wave generated? cm

Explanation / Answer

P = mu w^2 A^2 v / 2

P = (2 pi f)^2 A^2 sqrt(mu T)

everything is same except amplitude and linear mass density are changing.

so A^2 sqrt(mu) = constant

6^2 sqrt(5.60 x 10^-2) = A^2 sqrt(2.70 x 10^-2)

A = 7.2 cm .........Ans

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