The distance between any two adjacent nodes in a stationary wave is 15 cm. if the speed of the wave is 294 ms/, what is its frequency?

Explanation

To solve the problem, we need to find the frequency of a stationary wave given the distance between two adjacent nodes and the speed of the wave.

### Step-by-Step Solution:

**Step 1: Understand the relationship between nodes and wavelength.**
- In a stationary wave, the distance between two adjacent nodes is half of the wavelength (λ). Therefore, if the distance between two adjacent nodes is given as 15 cm, we can express this mathematically as:
\[ \frac{\lambda}{2} = 15 \text{ cm} \]

**Step 2: Calculate the wavelength (λ).**
- To find the full wavelength (λ), we multiply both sides of the equation by 2:
\[ \lambda = 2 \times 15 \text{ cm} = 30 \text{ cm} \]
- Convert centimeters to meters (since the speed is given in meters per second):
\[ \lambda = 30 \text{ cm} = 0.30 \text{ m} \]

**Step 3: Use the wave speed formula to find frequency.**
- The formula that relates wave speed (v), frequency (f), and wavelength (λ) is:
\[ v = f \cdot \lambda \]
- We can rearrange this formula to solve for frequency (f):
\[ f = \frac{v}{\lambda} \]

**Step 4: Substitute the known values into the frequency formula.**
- Given that the speed of the wave (v) is 294 m/s and the wavelength (λ) is 0.30 m:
\[ f = \frac{294 \text{ m/s}}{0.30 \text{ m}} \]

**Step 5: Calculate the frequency.**
- Performing the division:
\[ f = 980 \text{ Hz} \]

### Final Answer:
The frequency of the wave is **980 Hz**.

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