What is the wavelength of a wave with a speed of 12 m/s and a period of 0.25 s?

Options

A. 0.25m
B. 1.5m
C. 3.0m
D. 24m

Answer

To find the wavelength of a wave given its speed and period, we can follow these steps:

### Step 1: Understand the relationship between speed, frequency, and wavelength
The speed of a wave (V) is related to its frequency (f) and wavelength (λ) by the formula:
\[ V = f \cdot \lambda \]

### Step 2: Relate frequency to the period
Frequency (f) is the reciprocal of the period (T):
\[ f = \frac{1}{T} \]
Given that the period \( T = 0.25 \) seconds, we can calculate the frequency.

### Step 3: Calculate the frequency
Using the formula for frequency:
\[ f = \frac{1}{T} = \frac{1}{0.25} = 4 \text{ Hz} \]

### Step 4: Substitute the values into the wave speed equation
Now that we have the frequency, we can substitute it back into the wave speed equation:
\[ V = f \cdot \lambda \]
We know \( V = 12 \text{ m/s} \) and \( f = 4 \text{ Hz} \). We can rearrange the equation to solve for wavelength (λ):
\[ \lambda = \frac{V}{f} \]

### Step 5: Calculate the wavelength
Substituting the known values:
\[ \lambda = \frac{12 \text{ m/s}}{4 \text{ Hz}} = 3 \text{ m} \]

### Conclusion
The wavelength of the wave is \( \lambda = 3 \text{ m} \).

---