The wave equation for a standing wave on a string fixed at both ends is $y ( x , t ) = 24 \cos ( 3.0 x ) \cos ( 2 t )$ cm. The speed of the traveling waves that result in this standing wave is
A) 0.67 m/s.
B) 1.5 m/s.
C) 8.0 m/s.
D) 1.5 cm/s.
E) 0.67 cm/s.

Question

Quizplus · Accepted Answer

The wave speed is given by v = f\lambda, where f is the frequency and \lambda is the wavelength. The wavelength is given by \lambda = 2L/n, where L is the length of the string and n is the number of nodes. In this case, n = 2, so \lambda = L. The frequency is given by f = 2\pi/T, where T is the period. The period is given by T = 1/f, so f = 1/T. Substituting these expressions into the wave speed equation, we get v = f\lambda = (1/T)(L) = (2\pi/T)(L) = 2\pi f L. In this case, f = 2 Hz and L = 1 m, so v = 2\pi (2 Hz) (1 m) = 4\pi m/s = 1.5 m/s.

The Wave Equation for a Standing Wave on a String y(x,t)=24cos⁡(3.0x)cos⁡(2t)y ( x , t ) = 24 \cos ( 3.0 x ) \cos ( 2 t )y(x,t)=24cos(3.0x)cos(2t)

The Wave Equation for a Standing Wave on a String $y ( x , t ) = 24 \cos ( 3.0 x ) \cos ( 2 t )$