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dibilo
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i've found 2 equations on longitudinal velocity of waves v=lambda*freq and v=Lsqrt(k/m). is the 2nd equation derived from the 1st? if not how do you derive it? thx.
The second equation for wave longitudinal velocity is v = √(B/ρ), where v is the velocity, B is the bulk modulus, and ρ is the density.
The second equation is derived using the equation for wave velocity in a general elastic medium, v = √(E/ρ), where E is the Young's modulus. By substituting B = E/3, which is the relationship between the bulk modulus and Young's modulus for solids, we can derive the second equation.
The second equation is significant because it allows scientists and engineers to calculate the velocity of longitudinal waves in a medium using only the bulk modulus and density, without needing to know the material's Young's modulus.
No, the second equation is specifically for longitudinal waves, which are waves that vibrate parallel to the direction of propagation. It cannot be applied to transverse waves, which vibrate perpendicular to the direction of propagation.
The first equation for wave velocity, v = √(E/ρ), is a more general equation that applies to both longitudinal and transverse waves. The second equation is a simplified version that only applies to longitudinal waves. In cases where the material's Young's modulus is known, the first equation should be used for calculations.