Question

Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave: y(x,t) = (11.4 cm) * sin(3.9*x - 53.6 s-1*t + 0.11 rad); with x in meters and t in seconds. What is the phase difference between them?What is their amplitude? What is their period?

Answer 1

answer) the following equation is in the form

Yx,t=2ym cos($\phi$/2)sin( kx-$\omega$t+$\phi$/2)

a) on comparing we have

$\phi$/2=0.11 rad

$\phi$=0.11*2=0.22rad

so the answer is 0.22rad

b) again on comparison

2ym cos($\phi$/2)=11.4cm

2ym cos (0.11 )=11.4cm

ym=5.73 cm

so the answer is 5.73cm or 5.7 cm

c) again on comparison

2pi=$\omega$T

T=2pi/$\omega$=2pi/53.6=0.117 s

so the answer 0.117 s or 0.12 s