ps04 - Physics 214 Problem Set #4 (Due 11:15 am, Thursday...

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Page 1 of 2 Physics 214 Problem Set #4 (Due 11:15 am, Thursday 9/25/08) 1. In lecture, we showed that the displacement s ( x , t ) in a one-dimensional sound wave satisfies the wave equation: 22 2 2 2 // st sx ∂∂ =∂∂ v , where 2 / B ρ = v . Starting with the wave equation for s ( x , t ) and the relationship between pressure and displacement, show that pressure variation p ( x , t ) must also satisfy a wave equation of the same form with the same wave speed: 2 p tp x = v . Therefore, we can equally well describe a 1-D sound wave using s ( x , t ) or p ( x , t ). [Hint: take / x ∂ ∂ of both sides of the wave equation for s ( x , t ).] 2. Consider a spring that obeys Hooke's law with spring constant κ , total mass M , and relaxed (unstretched) length L 0 . The spring is stretched to a length L > L 0 and its ends attached to keep it under tension. We want to derive the wave equation for longitudinal waves on the spring and to find the wave speed. Consider , M , L 0 , and L to be known quantities.
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ps04 - Physics 214 Problem Set #4 (Due 11:15 am, Thursday...

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