y(x,t)=(0.750 cm)cos[π(0.400 rad/cm)x+(250 rad/s)t].
a) The amplitude is 0.750 cm.
b) Note the angular frequency before time variable:
ω=250 rad/s, T=ω2π=0.025 s.
c) The frequency is
f=2πω=29.8 Hz.
d) The wavelength can be found from the wave number:
k=0.4π rad/cm, λ=k2π=5 cm.
e) The speed:
v=kω=198.9 cm/s.
f) Since the wave number is positive, the direction is also positive.
g) The tension:
T=v2μ=1.992⋅50⋅10−3=0.198 N.
h) Just substitute the values (substitute x in centimeters):
y(x,t)=0.75cos[0.4π⋅56.4+250⋅0.115]=−0.125 cm.
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