The equation representing a wave on a string is y(x,t)= 0.23 m cos((23.2 m^-1)x - (15.3s^-1)t).What is the wave velocity? A)1.5 m/s right B)0.66 m/s right C)1.5 m/s left D)0.66 m/s left E)None are correct.

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Quizplus · Accepted Answer

The wave velocity can be found by the equation v = λf, where λ is the wavelength and f is the frequency. The general form of a wave equation is y(x,t) = A sin(kx - ωt) or y(x,t) = A cos(kx - ωt), where k is the wave number (2π/λ) and ω is the angular frequency (2πf). Comparing this equation to the given equation, we have k = 23.2 m^{-1} and ω = 15.3 s^{-1}. Therefore, the wavelength is λ = 2π/k = 0.271 m and the frequency is f = ω/2π = 2.43 Hz. Hence, the wave velocity is v = λf = 0.66 m/s to the right. Thus, the correct answer is B.

The Equation Representing a Wave on a String Is Y(x,t)=