To solve the problem of finding the velocity of waves, we need to follow these steps:
1. Determine the frequency of the waves:
- Frequency is defined as the number of waves that pass a given point in a specific amount of time.
- The formula to calculate frequency is:
[tex]\[
\text{Frequency} = \frac{\text{Number of waves}}{\text{Time (seconds)}}
\][/tex]
- Given that the number of waves is 25 and the time is 10 seconds, we can substitute these values into the formula:
[tex]\[
\text{Frequency} = \frac{25}{10}
\][/tex]
- By performing the division, we get:
[tex]\[
\text{Frequency} = 2.5 \, \text{waves per second}
\][/tex]
2. Calculate the velocity of the waves:
- The velocity of a wave is calculated by multiplying the frequency by the wavelength.
- The formula to calculate velocity is:
[tex]\[
\text{Velocity} = \text{Frequency} \times \text{Wavelength}
\][/tex]
- Given that the frequency is 2.5 waves per second and the wavelength is 50 cm, we can substitute these values into the formula:
[tex]\[
\text{Velocity} = 2.5 \, \text{waves per second} \times 50 \, \text{cm}
\][/tex]
- By performing the multiplication, we get:
[tex]\[
\text{Velocity} = 125 \, \text{cm per second}
\][/tex]
Therefore, the velocity of the waves is [tex]\( \boxed{125 \text{ cm per second}} \)[/tex]. This matches the last option provided in the question.
