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 ?

Answer

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

### Step 1: Understand the relationship
The fundamental frequency (f₀) of a stretched wire is given by the formula:
\[ f_0 = \frac{V}{2L} \]
where:
- \( f_0 \) = fundamental frequency (in Hz)
- \( V \) = speed of the wave (in m/s)
- \( L \) = length of the wire (in meters)

### Step 2: Rearrange the formula to find the speed
To find the speed \( V \), we can rearrange the formula:
\[ V = 2L \cdot f_0 \]

### Step 3: Substitute the known values
We are given:
- Length of the wire \( L = 1 \, \text{m} \)
- Fundamental frequency \( f_0 = 300 \, \text{Hz} \)

Now, substitute these values into the rearranged formula:
\[ V = 2 \cdot 1 \cdot 300 \]

### Step 4: Calculate the speed
Now, perform the calculation:
\[ V = 2 \cdot 1 \cdot 300 = 600 \, \text{m/s} \]

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

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