The speed of a wave is 340 `ms^(-1)` . What is the wavelength of the wave if its frequency is 500 Hz?

Options

A. 0.68 m
B. 6.8 m
C. 68 m
D. 0.068 m

Answer

To find the wavelength of a wave when the speed and frequency are given, we can use the formula that relates speed (v), frequency (ν), and wavelength (λ):

### Step-by-Step Solution:

1. **Identify the given values:**
- Speed of the wave, \( v = 340 \, \text{m/s} \)
- Frequency of the wave, \( \nu = 500 \, \text{Hz} \)

2. **Use the wave equation:**
The relationship between speed, frequency, and wavelength is given by the equation:
\[ v = \nu \cdot \lambda \]
where:
- \( v \) is the speed of the wave,
- \( \nu \) is the frequency,
- \( \lambda \) is the wavelength.

3. **Rearrange the equation to solve for wavelength (λ):**
To find the wavelength, we can rearrange the equation:
\[ \lambda = \frac{v}{\nu} \]

4. **Substitute the known values into the equation:**
Now, substitute the values of \( v \) and \( \nu \):
\[ \lambda = \frac{340 \, \text{m/s}}{500 \, \text{Hz}} \]

5. **Perform the calculation:**
\[ \lambda = \frac{340}{500} = 0.68 \, \text{m} \]

6. **Conclusion:**
The wavelength of the wave is \( 0.68 \, \text{m} \).

### Final Answer:
The wavelength of the wave is \( 0.68 \, \text{m} \).

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