Question

3. The speed of light in vacuum is approximately 3 × 108 m/s. Find the wavelength of red light having a frequency of 5 x 1014 Hz. Compare this with the wavelength of a 60-Hz electromagnetic wave. 4. A youngster in a boat on a lake watches waves that seem to be an endless succession of identical crests passing with a half-second interval between each. If every disturbance takes 1.5 s to sweep straight along the length of her 4.5-m-long boat, what are the frequency, period, and wavelength of the waves? 5. Calculate the speed (phase velocity) of the wave whose representation in SI units is wy,t) = A cos(3 * 10y +9 * 1014 t) 6. The electric field of an electromagnetic plane wave is given in SI units by Ē = Ē.e-i(3x-vāy-9.9+10%t) (a) What is the wave's angular frequency? (b) Write an expression for k. (c) What is the value of k? (d) Determine the speed of the wave.

Answer 1

please note : value of k is 3.32 , which is squre root of 11 , and which is modulus of wave vector k. Thanks

1. So, by : d = 4 d: 371 - 9.6 10 5710"" 0.6410 64100m so, Warelungn dia 67169m Now wamelength of En wan with frequency v= 6olHz di 370€ 300.x10 = 5x100 meter Shop | 1»> din? 60 409,41 = Cos (3xjoby + 9x1814 +) Compare with y= Alas (ky + lot) ka gx106 waano'y so, prase velocity u = W/12 - du har Žxist = 3 xlo‘miste . : c=spect flight © £ = fo emp (-i ( 3n-Tay-99 WoB )] here, k = 3î - 52 ſ W = 9.grupos 2.7x10 m se (a) angular freueray & W= 94108radise (b) T's 31 -'raj :) 1K1 - 1972 - JIT, so, speedy wane =