Can you guys help me solve the rest? I\'m clueless A string vibrates according t
ID: 1513179 • Letter: C
Question
Can you guys help me solve the rest? I'm clueless
A string vibrates according to the equation Y(x, t) = 0.50 cm * sin((3.0cm^-1)x)*cos(8.0 rad/s)t What is the angular wave number? What is the wavelength? What is the speed of the 2 waves making the standing wave? What is the amplitude of the 2 waves making the standing wave? What is the distance between the nodes? What is the angular speed of the 2 waves making the standing wave? What is the period of the 2 waves making the standing wave? What is the maximum transverse speed of this standing wave? Write the equations for the two waves making up the standing waveExplanation / Answer
y(x,t) =0.5 cm sin(3x) cos(8t)
comparing with general wave equation
y(x,t) = A sin(kx) cos(wt)
angular wave number k = 3 rad/cm
k = 2pi/lamda = 2*3.14/lamda = 3 rad/cm
lamda = 2.093 cm
wavelength = 2.093 cm
speed of wave v = w/k = 8/3 = 2.67 cm/s
2A = 0.5 cm
amplitude A = 0.25 cm
distance between nodes = lamda/2 = 2.093/2 = 1.0465 cm
angulae speed w = 8 rad/s
T = 2pi/w = 2*3.14/8 = 0.785 s
vmax = Aw = 0.25*8 = 2 m/s
y1(x,t) = 0.25 sin(3x - 8t)
y2(x,t) = 0.25 sin(3x+- 8t)