Question

The extension in a wire obeying Hooke’s law is \( x \). The speed of sound in the stretched wire is \( V \). If the extension in the wire is increased to \( 4x \), then the speed of sound in the wire is

• A. \( V \)
• B. \( 2.5V \)
• C. \( 2V \)
• D. \( 1.5V \)

Hint:

When dealing with stretched wires, remember that the speed of sound is proportional to the square root of the tension in the wire.

Answer 1

The Correct Option is C

Step 1: Formula for the speed of sound in a stretched wire.
The speed of sound in a wire depends on the tension in the wire and the mass per unit length. The relationship is given by: \[ V \propto \sqrt{\frac{T}{\mu}} \] where \( T \) is the tension and \( \mu \) is the mass per unit length.
Step 2: Relationship between extension and tension.
Since the tension is directly proportional to the extension \( x \), if the extension is increased to \( 4x \), the tension will also increase by a factor of 4. Therefore, the speed of sound will increase by a factor of \( \sqrt{4} = 2 \).
Step 3: Conclusion.
Thus, the new speed of sound is (C) \( 2V \).