To find the speed of a water wave when you are given the frequency and the wavelength, follow these steps:
1. Understand the formula.
The speed [tex]\( v \)[/tex] of a wave can be calculated using the formula:
[tex]\[
v = f \cdot \lambda
\][/tex]
where [tex]\( f \)[/tex] is the frequency and [tex]\( \lambda \)[/tex] (lambda) is the wavelength.
2. Identify the given values.
- Frequency ([tex]\( f \)[/tex]): 5.0 Hz
- Wavelength ([tex]\( \lambda \)[/tex]): 10 cm
3. Convert the wavelength into standard units.
Since standard units for wavelength in the formula are typically in meters, you need to convert 10 cm to meters. Recall that 1 cm is equal to 0.01 meters:
[tex]\[
\lambda = 10 \text{ cm} \times 0.01 \frac{\text{meters}}{\text{cm}} = 0.1 \text{ meters}
\][/tex]
4. Calculate the speed.
Now, use the formula [tex]\( v = f \cdot \lambda \)[/tex]:
[tex]\[
v = 5.0 \text{ Hz} \times 0.1 \text{ meters}
\][/tex]
5. Perform the multiplication.
[tex]\[
v = 0.5 \text{ meters per second}
\][/tex]
So, the wavelength in meters is 0.1 meters, and the speed of the water wave is 0.5 meters per second.
