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Physics Problem Wire stretched with tension F. Transverse traveling waves of amplitude A, wavelength λ1 carry average power Pav1 = 0.700 W .?
A light wire is tightly stretched with tension F. Transverse traveling waves of amplitude A and wavelength λ1 carry average powerPav,1 = 0.700 W .
If the wavelength of the waves is doubled, so λ2 = 2λ1 while the tension F and amplitude A are not altered, what then is the average power Pav,2 carried by the waves?
Been stuck on this problem for quite some time and I m not sure where to start. Any help is appreciated.
Thank you in advanced
1 Answer
- ?Lv 73 years agoFavorite Answer
The speed (v) depends on the linear density (μ) and tension (F).
v = √(F/μ)
Since F and μ are unchanged v is unchanged.
Using the link, the formula for transmitted power is:
P = ½μω²A²v (see http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/p... )
Since μ, A (amplitude) and v are unchanged, P is proportional to ω²
______________
ω = 2πf and f = v/λ so ω = 2πv/λ
Since v doesn’t change ω is inversely proportional to λ.
λ is doubled, so ω is halved. ω² is quartered.
Pav2 = ¼Pav1 = 0.700/4 = 0.175W
