Answer:
so the transverse displacement is 0.089963 m
Explanation:
Given data
equation y(x,t)=Acos(kx−ωt)
speed v = 9.00 m/s
amplitude A = 9.00 × 10^−2 m
wavelength λ = 0.480 m
to find out
the transverse displacement
solution
we know
v = angular frequency / wave number
and
wave number = 2 / λ = 2
/ 0.480 = 13.0899
angular frequency = v k
angular frequency = 9.00 × 13.0899
angular frequency = 117.8097 rad/sec = 118 rad/sec
so
equation y(x,t)=Acos(kx−ωt)
y(x,t)=9.00 × 10^−2 cos(13.0899 x−118t)
when x =0 and and t = 0
maximum y(x,t)= 9.00 × 10^−2 cos(13.0899 (0) − 118 (0))
maximum y(x,t)= 9.00 × 10^−2 m
and when x = x = 1.59 m and t = 0.150 s
y(x,t)=9.00 × 10^−2 cos(13.0899 (1.59) −118(0.150) )
y(x,t)=9.00 × 10^−2 × (0.99959)
y(x,t) = 0.089963 m
so the transverse displacement is 0.089963 m