Answer
a. The wavelengths for the modes are λ=2L/m so
b. Wave Speed v =√(gλ)/(2ℼ)
c. v =√(gλ)/(2ℼ) = fλ = f(m)=√(g)/(2ℼλ) = √(mg)/(4ℼL)
d. Period of oscillation √(mg)/(4ℼL)
Work Step by Step
a. The wavelengths for the modes are λ=2L/m so
λ(1)=(2(10.0m))/1 = 20.0 m
λ(2)=(2(10.0m))/2 = 10.0 m
λ(3)=(2(10.0m))/3 = 6.67 m
The depth of the pool is 5.0 m so the λ(2) and λ(3) are deep water waves
b. Wave Speed v =√(gλ)/(2ℼ)
v(1) =√((9.8m/s²)(20.0m))/(2ℼ) = 5.6 m/s
v(2) = √((9.8m/s²)(10.0m))/(2ℼ) = 4.0 m/s
v(3) = √((9.8m/s²)(6.67m))/(2ℼ) =3.2 m/s
c. v =√(gλ)/(2ℼ) = fλ = f(m)=√(g)/(2ℼλ) = √(mg)/(4ℼL)
*m is mode
d. Period of oscillation
f(1) = √((1)(9.8 m/s²))/((4ℼ)(10.0m)) = 0.279 Hz --> 1/f = 3.6 s
T (2) = 2.5 s
T(3) = 2.1 s
