The velocity v of the wave set-up by plucking a stretched string is found to depend on the tension T
The velocity v of the wave set-up by plucking a stretched string is found to depend on the tension T in the string, its length l and its mass m, and is given by v = kTx ly mz where x, y and z are unknown numbers and k is a constant. Find x, y and z.
The velocity v of the wave set-up by plucking a stretched string is found to depend on the tension T in the string, its length l and its mass m, and is given by v = kTx ly mz where x, y and z are unknown numbers and k is a constant. Find x, y and z.
Use dimensions. Speed v = L T⁻¹. Tension T = M L T⁻². So (M L T⁻²)ˣ Lʸ Mᶻ must equal L T⁻¹.
Time: −2x = −1, so x = 1/2. Mass: x + z = 0, so z = −1/2. Length: x + y = 1, so y = 1/2.
So x = 1/2, y = 1/2, z = −1/2.
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