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Unformatted text preview: Quiz Solutions 1 Evaluate ω p . [2 Points] ω 2 p = n e e 2 m e = (2 × 10 8 m 3 )(1 . 6 × 10 19 C ) 2 (9 . 11 × 10 31 kg )(8 . 85 × 10 12 F m ) = 6 . 3505 × 10 5 C 2 m 2 kgF (1) Units : 1 C 2 m 2 kgF = 1 s 2 (2) ω p = . 0007969 Hz (3) 2 Find the phase velocity v ph . [2 Points] So we begin by looking at the dispersion relations we’ve been given ω 2 = ω 2 p + k 2 c 2 v ph = ω k = q ω 2 p + k 2 c 2 k = 1 k q ω 2 p + k 2 c 2 = r ω p k 2 + c 2 (4) 3 Find the group velocity v g . [2 Points] v g = dω dk = d dk q ω 2 p + k 2 c 2 = 1 2 ( ω 2 p + k 2 c 2 ) 1 / 2 (2 kc 2 ) = kc 2 q ω 2 p + k 2 c 2 (5) 4 Find the time difference in arrival times of two pulses moving through interstellar space with ω 1 = 1GHz and ω 1 = 2GHz. [2 Points] First we begin by putting the v g in terms of ω . We use v g because this is the speed at which a pulse will travel. v g = kc 2 q ω 2 p + k 2 c 2 (6) We now solve for k using the dispersion relation and plug into (6). k = √ ω 2 ω 2...
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 Spring '09
 DUDKO
 mechanics, Wavelength, group velocity, Wave propagation, dispersion relation

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