Let's break down the solution to this problem step by step:
### 1. Calculate the Wavelength (λ)
#### Given:
- The total length of 5 waves is [tex]\( 25 \)[/tex] cm.
To find the wavelength, we need to determine the length of a single wave. This can be calculated by dividing the total length of the waves by the number of waves.
[tex]\[
\lambda = \frac{\text{total length of waves}}{\text{number of waves}} = \frac{25 \text{ cm}}{5} = 5 \text{ cm}
\][/tex]
So, the wavelength is [tex]\( 5 \)[/tex] cm.
### 2. Calculate the Frequency (f)
#### Given:
- [tex]\( 5 \)[/tex] waves pass a point in [tex]\( 1 \)[/tex] second.
Frequency is defined as the number of waves passing a point per unit time. Using the given data:
[tex]\[
f = \frac{\text{number of waves}}{\text{time}} = \frac{5 \text{ waves}}{1 \text{ s}} = 5 \text{ Hz}
\][/tex]
So, the frequency is [tex]\( 5 \)[/tex] Hz.
### 3. Calculate the Period (T)
#### Given:
- Frequency [tex]\( f = 5 \)[/tex] Hz.
The period is the reciprocal of frequency. It represents the time taken for one complete wave to pass a point:
[tex]\[
T = \frac{1}{f} = \frac{1}{5 \text{ Hz}} = 0.2 \text{ s}
\][/tex]
So, the period is [tex]\( 0.2 \)[/tex] seconds.
### Summary:
a. The wavelength is [tex]\( 5 \)[/tex] cm.
b. The frequency is [tex]\( 5 \)[/tex] Hz.
c. The period is [tex]\( 0.2 \)[/tex] seconds.
