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The following physics responses are provided by a student and, as such, should be considered in that context. While every effort is made for accuracy, absolute correctness cannot be fully guaranteed.
| Question | |
C | 13 |
I | |
Question Tripling both the tension in a guitar string and its mass per unit length will result in changing the wave speed in the string by what factor? | |
Answer 1.00 (i.e., no change) | |
Notes
| User | Added | Note | e | d |
|---|---|---|---|---|
| KillGorack | 2023-07-16 15:34:56 | To determine the change in wave speed in the guitar string when both the tension and the mass per unit length are tripled, we can use the wave speed equation for transverse waves: v = √(T/μ) Let's assume the initial tension in the guitar string is T₁ and the initial mass per unit length is μ₁. After tripling both the tension and the mass per unit length, the new tension is 3T₁, and the new mass per unit length is 3μ₁. Using the wave speed equation, we can calculate the initial wave speed (v₁) and the new wave speed (v₂): v₁ = √(T₁/μ₁) v₂ = √((3T₁)/(3μ₁)) To find the factor by which the wave speed changes, we can divide v₂ by v₁: v₂/v₁ = √((3T₁)/(3μ₁)) / √(T₁/μ₁) v₂/v₁ = √((3T₁)/(3μ₁)) * √(μ₁/T₁) v₂/v₁ = √((3T₁μ₁)/(3T₁μ₁)) v₂/v₁ = √(1) v₂/v₁ = 1 Therefore, tripling both the tension and the mass per unit length in a guitar string will not change the wave speed. The wave speed remains the same. |
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