A wave on a string is described by D(x,t)=(3.6cm)× sin[2π(x/(8.4m)+t/(0.16s)+1)], where x is in m and t is in s.
A)In what direction is this wave traveling?
B) What is the wave speed?
C)What is the frequency?
D)What is the wave number?
E) At t=0.24s, what is the displacement of the string at x=9.1m?
D(x,t)=(3.6cm)× sin[2π(x/(8.4m)+t/(0.16s)+1)]
We compare this equaiton with
y = A sin(kx+wt) (moves in negative x direction)
Here A = 3.6 cm, k = 2π/8.4 , w = 2π/0.16,
(a) Wave is travelling in negative x direction.
(b) Wave speed v =w/k
v = ( 2π/0.16)/ ( 2π/8.4)
v = 8.4/0.16 = 52.5 m/s
(c) w =2πf = 2π/0.16
f =1/0.16 = 6.25 Hz
(d) k = ( 2π/8.4) =0.75 /m
(e) D(x,t)=(3.6cm)× sin[2π(x/(8.4m)+t/(0.16s)+1)]
t =0.24 s, x =9.1
D(x,t)=(3.6cm)× sin[2π(9.1/(8.4m)+0.24/(0.16s)+1)]
D(x,t)=(3.6cm)× sin[2π(1.083+1.5+1)]
D(x,t)=(3.6cm)× sin(22.5)
D(x,t)= 1.38 cm
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