Velocity of Wave in Twice the Radius String: V = root(Tension/mu) * root2

AI Thread Summary
A wave traveling along a string at 280 m/s will have its speed affected when the string is replaced with one of the same material and tension but with twice the radius. The velocity formula V = √(Tension/μ) indicates that μ, the mass per unit length, changes when the radius is doubled, as the mass of the string also doubles. The discussion reveals confusion over whether the wave speed should be halved or multiplied by √2 when the radius increases. It is clarified that while the mass increases, the manipulation of the formulas shows that the wave speed actually increases, leading to the conclusion that the new speed is 280 m/s multiplied by √2. Understanding these relationships is crucial for accurately determining wave speed in varying string conditions.
lostie100
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A wave travels along a string at a speed of 280m/s. What will the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius?

V = root (Tension/mu)

mu = mass/length

length is 2radii

I manipulated the formulas, however, apparently you divide the velocity by 2, but I found it to be multiplied by root2.
Please show me the manipulation of the formulas...
 
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Assuming uniform density what happens when you double the cross-section of the string that remains the same length? Does the total mass of the string change? By how much?

Plug in your numbers then and see what happens.
 
The mass also doubles...but I don't see how it relates to the other formula for velocity...
 
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