Calculating Period T in Terms of pi, λ, and g

[sphouxay]

Homework Statement

Find the period T for a wave of wavelength (lambda) .
Express the period in terms of pi, lambda , and g.

Homework Equations

T = lambda/velocity,
lambda = velocity/frequency
T= 1/frequency
k (wave number) = 2pi/lambda
V = Squareroot of (g/k)

The Attempt at a Solution

Ive tried several attempts but nothing leads me to the terms I needed alone. More will be added later if I find out.

 

[Redbelly98]

Homework Equations

T = lambda/velocity,
lambda = velocity/frequency
T= 1/frequency
k (wave number) = 2pi/lambda
V = Squareroot of (g/k)

The Attempt at a Solution

Ive tried several attempts but nothing leads me to the terms I needed alone. More will be added later if I find out.

As you said, T = λ/V. This is a good starting point.
Next, you can use your expression for V here.

 

[Mene]

One possible solution could be to use the equation T = 1/frequency and substitute in the equation for frequency given by lambda = velocity/frequency. This would give us T = 1/(lambda/velocity), which simplifies to T = velocity/lambda. Then, we can use the equation for wave number, k = 2pi/lambda, and substitute it into the equation for velocity, V = √(g/k). This gives us V = √(g/(2pi/lambda)), which can be rearranged to λ = 2piV^2/g. Finally, we can substitute this value of lambda into our initial equation for period, giving us T = (velocity)/(2piV^2/g). This expresses the period T in terms of pi, lambda, and g.