Distance between nodes on a string is 5 cm. Velocity of transverse wave is `2ms^(-1)`. Then the frequency is

Options

A. 5 Hz
B. 10 Hz
C. 20 Hz
D. 15 Hz

Explanation

To solve the problem step by step, we will use the information given about the distance between nodes, the velocity of the wave, and the relationship between frequency, wavelength, and velocity.

### Step 1: Understand the relationship between nodes and wavelength
The distance between two consecutive nodes in a standing wave is equal to half the wavelength (λ/2).

### Step 2: Given data
From the question, we know:
- Distance between nodes = 5 cm = 0.05 m (convert to meters for consistency)
- Velocity of the wave (v) = 2 m/s

### Step 3: Calculate the wavelength (λ)
Since the distance between nodes is λ/2:
\[ \frac{\lambda}{2} = 0.05 \, \text{m} \]
To find λ, we multiply both sides by 2:
\[ \lambda = 2 \times 0.05 \, \text{m} = 0.1 \, \text{m} \]

### Step 4: Use the wave velocity formula
The relationship between velocity (v), frequency (f), and wavelength (λ) is given by the formula:
\[ v = f \cdot \lambda \]
We can rearrange this formula to find the frequency:
\[ f = \frac{v}{\lambda} \]

### Step 5: Substitute the known values
Now, substitute the values of velocity and wavelength into the frequency formula:
\[ f = \frac{2 \, \text{m/s}}{0.1 \, \text{m}} = 20 \, \text{Hz} \]

### Final Answer
The frequency of the transverse wave is **20 Hz**.

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