The wave function for a wave on a taut string is given below, where x is in mete
ID: 1751020 • Letter: T
Question
The wave function for a wave on a taut string is given below, wherex is in meters and t is in seconds. y(x, t) = (0.340 m) sin(10t - 3x +/4) (a) What is the average rate at which energy istransmitted along the string if the linear mass density is 75.0g/m?Enter anumber. 1 W
(b) What is the energy contained in each cycle of the wave?
Enter anumber. 2 J y(x, t) = (0.340 m) sin(10t - 3x +/4) (a) What is the average rate at which energy istransmitted along the string if the linear mass density is 75.0g/m?
Enter anumber. 1 W
(b) What is the energy contained in each cycle of the wave?
Enter anumber. 2 J Enter anumber. Enter anumber.
Explanation / Answer
(a)If the tension in the string is T and its mass per unitlength is ,the wave speed,is v = (T/) or v^2 = (T/) or T = v^2 * the maximum speed of the wave vmax= A * w A = 0.340 m w = 10 s-1 the average rate at which energy is transmitted along thestring if the linear mass density is = 75.0 g/m = 75.0 * 10^-3 kg/m is P = T * vmax or P = vmax^2 * * vmax=vmax^3 * (b)the energy contained in each cycle of the wave E = P * T T is the time period of the wave the angular frequency w = 2f = (2/T) or (2/T) = 10 or T = (1/5) = 0.2 s or E = vmax^3 * * T or P = vmax^2 * * vmax=vmax^3 * (b)the energy contained in each cycle of the wave E = P * T T is the time period of the wave the angular frequency w = 2f = (2/T) or (2/T) = 10 or T = (1/5) = 0.2 s or E = vmax^3 * * TRelated Questions
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