A sonometer wire , `100 cm` in length has fundamental frequency of `330 Hz`. The velocity of propagation of tranverse waves along the wire is

Options

A. `330 m//s`
B. `660 m//s`
C. `115 m//s`
D. `990 m//s`

Explanation

To find the velocity of propagation of transverse waves along the sonometer wire, we can follow these steps:

### Step 1: Understand the Setup
The sonometer wire is fixed at both ends, which means that it will have nodes at both ends and an antinode in the middle when vibrating in its fundamental mode.

### Step 2: Determine the Wavelength
In the fundamental mode of vibration for a wire fixed at both ends, the length of the wire corresponds to half of the wavelength (λ). Therefore, we can express this relationship as:
\[ L = \frac{\lambda}{2} \]
where \( L \) is the length of the wire.

Given that the length of the wire is 100 cm (or 1 meter), we can rearrange the equation to find the wavelength:
\[ \lambda = 2L = 2 \times 1 \text{ m} = 2 \text{ m} \]

### Step 3: Use the Frequency to Find Velocity
The velocity (v) of a wave is given by the formula:
\[ v = f \times \lambda \]
where \( f \) is the frequency and \( \lambda \) is the wavelength.

Given that the fundamental frequency \( f \) is 330 Hz, we can substitute the values into the equation:
\[ v = 330 \text{ Hz} \times 2 \text{ m} \]

### Step 4: Calculate the Velocity
Now, we perform the multiplication:
\[ v = 660 \text{ m/s} \]

### Final Answer
The velocity of propagation of transverse waves along the wire is \( 660 \text{ m/s} \).

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