A water wave traveling in a straight line on a lake is described by the equation

Question

A water wave traveling in a straight line on a lake is described by the equation

where y is the displacement perpendicular to the undisturbed surface of the lake.

a)How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor? t=?s

b)What horizontal distance does the wave crest travel in that time?s=?m

c)What is the wave number? k=? rad/cm

d)What isthe number of waves per second that pass the fisherman? f=? waves/s

e)How fast does a wave crest travel past the fisherman? v=?m/s

f)What is the maximum speed of his cork floater as the wave causes it to bob up and down? v(max)=?m/s

A water wave traveling in a straight line on a lake is described by the equation y(x,t)=(3.75cm)cos(0.450cm^(?1)x+5.40s^(?1)t) y(x,t) = )3.75cm)cos(0.450cm^-1 x + 5.40s^-1t) where y is the displacement perpendicular to the undisturbed surface of the lake. a)How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor? t=?s b)What horizontal distance does the wave crest travel in that time?s=?m c)What is the wave number? k=? rad/cm d)What isthe number of waves per second that pass the fisherman? f=? waves/s e)How fast does a wave crest travel past the fisherman? v=?m/s f)What is the maximum speed of his cork floater as the wave causes it to bob up and down? v(max)=?m/s

Explanation / Answer

y(x,t)=(3.75cm)cos(0.450cm^(?1)x+5.40s^(?1)t)
compare with standard equation
y = A cos( kx + wt )

A = 3.75 cm
K = 0.450 rad/cm
w = 5.40 rad/s

a)
T = 2pi/w = 6.28/5.40 = 1.162 sec
b)
wavelenght Lamda = 2pi/K = 6.28/0.450 = 13.955 cm = 0.13955 m
c)
K = 0.450 rad/cm
d)
frequecy f = w/2pi = 5.40/6.28 = 0.8598 waves/s
e)
wave speed V = w/k = 5.40/0.450 = 12 cm/s = 0.12 m/s
f)
Vmax = wA = 5.40*3.75*10^-2 = 0.2025 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.