Flag Wave Motion> Two waves, each having a frequency of 100100 Hz and a
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Two waves, each having a frequency of 100100 Hz and a wavelength of 22.00 cm, are travelling in the same direction on a string. What is the phase difference between the waves aa if the second wave was produced 00.015015 s later than the first one at the same instant but the first one was produced a distance 44.00 cm behind the second one? cc If each of the waves has an amplitude second one? cc If each of the waves has an amplitude of 22.00 mm, what would be the amplitude of the resultant waves in part aa and bb?

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Hrishant Goswami , 10 Years ago
Grade 10
anser 1 Answer
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Deepak Patra

Last Activity: 10 Years ago

Sol. f = 100 Hz, λ = 2 cm = 2 * 10 base 2 mrn∴ wave speed, v = f λ = 2 m/srna in 0.015 sec 1^ST wave has travelledrnx = 0.015 * 2 = 0.03 m = path diffnrn∴ corresponding phase difference, ∅ = 2π*/λ = 2π/ 2 * 10^2 * 0.03 = 3π.rnb Path different x = 4 cm = 0.04 mrn⇒ ∅ = π/λx = 2π/2 * 10^2 * 0.04 = 4 π.rnC The waves have same frequency, same wavelength and same amplitudernLet, Y base 1 = r sin wt y base 2 = r sin wt + ∅rn⇒ Y = Y base 1 + y base 2 = [r sin wt + wt + ∅rn= 2r sin wt + ∅/2 cos ∅/2rn∴ resultant amplitude = 2r cos ∅/2rnSo when ∅ = 3π, r = 2 * 10^ 3 m rnrnR base res = 2 * 2 * 10^3 cos 3π/2 = 0rnAgain, when ∅/2π, R base res = 2 * 2 * 10^3 cos 4π/2 = 4mm.

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