I have done some of this work myself but i just wanted to doublecheck with someb

Question

I have done some of this work myself but i just wanted to doublecheck with somebody: This is my problem: A sound wave isdescribed by ! D(y, t) = (0.20mm) sin[(8.96rad/m)y + (3140rad/m)t + "/4rad] where y is in meters and t is in seconds. a) In which direction is this wave traveling? b) Along which axis is the air oscillating? c) What are the wavelength, the wave speed, and the period ofoscillation? d) Draw a displacement vs. time graph D(y = 1 m, t) from t = 0s to t = 0.004 s. ! D(y, t) = (0.20mm) sin[(8.96rad/m)y + (3140rad/m)t + "/4rad] where y is in meters and t is in seconds. a) In which direction is this wave traveling? b) Along which axis is the air oscillating? c) What are the wavelength, the wave speed, and the period ofoscillation? d) Draw a displacement vs. time graph D(y = 1 m, t) from t = 0s to t = 0.004 s.

Explanation / Answer

Given D(y, t) = (0.20mm) sin[(8.96rad/m)y + (3140rad/m)t + "/4rad]    ---( 1) (a). The wave travel along negative axis (b).negative y-axis (c).compare eq( 1) with D(y,t ) = A sin [ ky + wt +] we get Amplitude A = 0.2 mm Propagation constant k = 8.96 rad / m Angular frequency w = 3140 rad / s So, wavelength = 2 / k                           = 0.7012 m wave speed v = w / k                       = 350.44 m / s Period T = 2 / w               = 0.002 s we get

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