When the tension in a wire is increased by a factor of 9, the speed of transverse waves traveling along the wire becomes 3 times the original speed. This relationship is derived from the equation v = √(T/m), where v represents wave speed, T represents tension, and m represents linear density. The correct answer is option c. 3v.
When the tension in a wire is increased, the speed of transverse waves traveling along the wire also changes. The relationship between tension (T), linear density (m), and wave speed (v) can be described by the equation:
v = √(T/m)
Let's analyze the given scenario step by step:
1. Initially, the tension in the wire is T, and the speed of the waves is v. The equation can be written as:
v1 = √(T/m)
2. When the tension is increased by a factor of 9, the new tension becomes 9T. We need to find the new speed of the waves, which we'll call v2.
v2 = √(9T/m)
3. To compare v1 and v2, let's simplify the equation for v2:
v2 = √(9T/m)
= 3 * √(T/m)
4. Comparing the equations for v1 and v2, we can see that the new speed v2 is equal to 3 times the original speed v1.
v2 = 3v1
5. Therefore, the speed of the waves when the tension is increased by a factor of 9 is 3 times the original speed.