The length of a stretched wire is 1 m and its fundamental frequency is 300 Hz.What is the speed of the transverse wave in the wire ?

Options

A. `330 m s^-1`
B. `600 m s^-1`
C. `990 m s^-1`
D. `550 m s^-1`

Answer

To find the speed of the transverse wave in the wire, we can use the relationship between frequency, speed, and length of the wire. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Length of the wire (L) = 1 m
- Fundamental frequency (f₀) = 300 Hz

### Step 2: Use the formula for fundamental frequency
The fundamental frequency of a stretched wire is given by the formula:
\[ f₀ = \frac{V}{2L} \]
where:
- \( V \) is the speed of the transverse wave in the wire,
- \( L \) is the length of the wire.

### Step 3: Rearrange the formula to solve for speed (V)
To find the speed \( V \), we can rearrange the formula:
\[ V = 2f₀L \]

### Step 4: Substitute the known values into the equation
Now, substitute the values of \( f₀ \) and \( L \) into the equation:
\[ V = 2 \times 300 \, \text{Hz} \times 1 \, \text{m} \]

### Step 5: Calculate the speed
Now, perform the calculation:
\[ V = 2 \times 300 \times 1 = 600 \, \text{m/s} \]

### Final Answer
The speed of the transverse wave in the wire is \( 600 \, \text{m/s} \).

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