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ODWE_1-10

# ODWE_1-10 - Tutorial ODWE One-Dimensional W Equation ave 5...

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Tutorial ODWE: One-Dimensional Wave Equation 5. Solutions to Exercises Exercise 1 . Transverse waves have the disturbance perpendicular to the direction of propagation of the disturbance. Don’t confuse the wave motion with the propagation. Exercise 2 . If the frequency is f; then in an amount of time, ¿ = 1 =f , a length, ¸ , of wave passes a given point. Thus, the speed of its passing is v = ¸= (1 =f ) = ¸f: Exercise 3 . The amplitude in the expression A cos · 2 ¼ ¸ ( x ¡ Àt ) + Á ¸ remains the same (i.e., the wave form moves in the direction of propagation) when x varies with time so as to keep the argument of the cosine function a constant. Thus, considering x to be a function of time, d dt · 2 ¼ ¸ ( x ¡ Àt ) + Á ¸ = 2 ¼ ¸ ( dx dt ¡ À ) = 0 = ) dx dt = + v: The positive sign means a velocity in the positive x direction, i.e., towardsthe right. If the argument were 2 ¼ ( x + Àt ) + Á , the constant argument condition would yield 2 ¼ ¸ ( dx dt + À ) = 0 = ) dx dt = ¡ v; indicating a velocity in the negative x direction.

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ODWE_1-10 - Tutorial ODWE One-Dimensional W Equation ave 5...

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