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Unformatted text preview: WebAssign Problems 1. Two points A and B on the surface of the Earth are at the same longitude and 60.0 ° apart in latitude. Suppose that an earthquake at point A creates a P wave that reaches point B by traveling straight through the body of the Earth at a constant speed of 7.80 km/s. The earthquake also radiates a Rayleigh wave, which travels along the surface of the Earth in an analogous way to a surface wave on water, at 4.50 km/s. (a) Which of these two seismic waves arrives at B first? (b) What is the time difference between the arrivals of the two waves at B ? Take the radius of the Earth to be 6 370 km. Solution: (a) The longitudinal wave travels a shorter distance and is moving faster, so it will arrive at point B first. (b) The wave that travels through the Earth must travel a distance of ( ) 6 6 2 sin30.0 2 6.37 10 m sin30.0 6.37 10 m R ° = × ° = × at a speed of 7 800 m/s Therefore, it takes 6 6.37 10 m 817 s 7 800 m s × = The wave that travels along the Earth’s surface must travel a distance of 6 rad 6.67 10 m 3 s R R π θ = = = × at a speed of 4 500 m/s Therefore, it takes 6 6.67 10 1482 s 4500 × = The time difference is 665 s 11.1 m in = 2. When a particular wire is vibrating with a frequency of 4.00 Hz, a transverse wave of wavelength 60.0 cm is produced. Determine the speed of waves along the wire. Solution: ( )( ) 4.00 H z 60.0 cm 240 cm s 2.40 m s v f λ = = = = 3. A sinusoidal wave train is described by y = (0.25 m) sin(0.30 x – 40 t ) where x and y are in meters and t is in seconds. Determine for this wave the (a) amplitude, (b) angular frequency, (c) angular wave number, (d) wavelength, (e) wave speed, and (f) direction of motion. Solution: ( ) 0.250sin 0.300 40.0 m y x t =- Compare this with the general expression ( ) sin y A kx t ω =- (a) 0.250 m A = (b) 40.0 rad s ω = (c) 0.300 rad m k = (d) 2 2 20.9 m 0.300 rad m k π π λ = = = (e) ( ) 40.0 rad s 20.9 m 133 m s 2 2 v f ω λ λ π...
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