### Theoretical reminder

We know that period $T$ is defined as the time required to complete one full cycle of a given motion.
The frequency $f$ is the number of oscillations per unit time.

They are related by the following formula:

$$
begin{equation}
f = frac{1}{T}
end{equation}
$$

We know that the wavelength and frequency determine the speed of a wave. They are related by the following formula:

$$
begin{equation}
v = lambda cdot f
end{equation}
$$

section*{Calculation}
begin{enumerate}[a)]
item
Our wave oscillates $n = 4$ times a second so the frequency is found directly:
begin{align*}
f = frac{n}{t} = frac{4}{1text{ s}} = 4text{ Hz}
end{align*}
item
The period is found using formula (1) as follows:
begin{align*}
T = frac{1}{f} = frac{1}{4text{ Hz}} = 0.25text{ s}
end{align*}
item
Since we know the frequency from part a, and we know the wavelength to be equal $lambda = 3.0text{ m}$, the speed of the wave can be determined using the formula (2) as follows:
begin{align*}
v = lambda cdot f = 3text{ m} cdot 4text{ Hz} = 12 ; frac{text{m}}{text{s}}
end{align*}
end{enumerate}

begin{enumerate}[a)]
item
The frequency is $f = 4text{ Hz}$
item
The period is $T = 0.25text{ s}$
item
The speed of the wave is $v = 12 ; frac{text{m}}{text{s}}$
end{enumerate}

### Theoretical reminder

We know that period $T$ is defined as the time required to complete one full cycle of a given motion.
The frequency $f$ is the number of oscillations per unit time.

They are related by the following formula:

$$
begin{equation}
f = frac{1}{T}
end{equation}
$$

We know that the wavelength and frequency determine the speed of a wave. They are related by the following formula:

$$
begin{equation}
v = lambda cdot f
end{equation}
$$

section*{Calculation}
begin{enumerate}[a)]
item
Our wave oscillates $n = 2$ times a second so the frequency is found directly:
begin{align*}
f = frac{n}{t} = frac{2}{1text{ s}} = 2text{ Hz}
end{align*}
item
The period is found using formula (1) as follows:
begin{align*}
T = frac{1}{f} = frac{1}{2text{ Hz}} = 0.5text{ s}
end{align*}
item
Since we know the frequency from part a, and we know the speed to be equal $v = 5.0 ; frac{text{m}}{text{s}}$, the wavelength of the wave can be determined using the formula (2) as follows:
begin{align*}
v = lambda cdot f \
end{align*}
Rearranging for $lambda$ we get:
begin{align*}
lambda = frac{v}{f}
end{align*}
Plugging in the numbers we get:
begin{align*}
lambda = frac{5 ; frac{text{m}}{text{s}}}{2text{ Hz}} = 2.5text{ m}
end{align*}
end{enumerate}

begin{enumerate}[a)]
item
The frequency is $f = 2text{ Hz}$
item
The period is $T = 0.5text{ s}$
item
The wavelength of the wave is $lambda = 2.5text{ m}$
end{enumerate}