The distance between two consecutive in a stationary wave is 25 cm . If the speed of the wave is `300 ms^(-1)`, calculate the frequency.

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the relationship between nodes and wavelength
In a stationary wave, the distance between two consecutive nodes is half of the wavelength (λ). Therefore, if the distance between two nodes is given as 25 cm, we can express this relationship mathematically.

### Step 2: Calculate the wavelength (λ)
Given that the distance between two nodes is 25 cm:
\[ \frac{\lambda}{2} = 25 \text{ cm} \]
To find the wavelength (λ), we multiply both sides by 2:
\[ \lambda = 2 \times 25 \text{ cm} = 50 \text{ cm} \]
Now, convert 50 cm to meters:
\[ \lambda = 50 \text{ cm} = 0.50 \text{ m} \]

### Step 3: Use the wave speed formula
The relationship between wave speed (v), frequency (f), and wavelength (λ) is given by the formula:
\[ v = f \cdot \lambda \]
We need to rearrange this formula to solve for frequency (f):
\[ f = \frac{v}{\lambda} \]

### Step 4: Substitute the values
We know the speed of the wave (v) is 300 m/s and the wavelength (λ) is 0.50 m. Now substitute these values into the frequency formula:
\[ f = \frac{300 \text{ m/s}}{0.50 \text{ m}} \]

### Step 5: Calculate the frequency
Now perform the division:
\[ f = 600 \text{ Hz} \]

Thus, the frequency of the wave is **600 Hz**.

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