Question

The tension in a wire clamped at both ends is doubled without appreciably changing the wire's length between the clamps.What is the ratio of the new to the old wave speed for transverse waves traveling along this wire?

Answer 1

Upon doubling the tension in a wire without changing its length, the wave speed increases by a factor of √2, making the new to old wave speed ratio approximately 1.414.

Step-by-step explanation:

The question revolves around the wave speed in a wire when its tension is altered. The wave speed (v) on a string or wire depends on the tension (T) and the linear mass density (μ), which can be described by the formula v = √(T/μ). When the tension is doubled, provided that the length and linear mass density remain constant, the new wave speed is given by vnew = √(2T/μ). Since the relationship between wave speed and tension is square root proportional, the new wave speed is √2 times the old wave speed. Therefore, if the initial wave speed is vold, then the ratio of the new to the old wave speed is vnew/vold = √2, or approximately 1.414.