Deriving the 2nd Equation on Wave Longitudinal Velocity

In summary, the first equation, v=lambda*freq, is a general property of waves while the second equation, v=Lsqrt(k/m), is derived from the properties of the medium. The second equation is derived by modelling a medium as a series of discrete particles and solving the equation of motion for these particles.
  • #1
dibilo
47
0
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.
 
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  • #2
The first is a general property of waves but the second appears to be based on the properties based on the properties of the medium. You gave no indication of what the physical situation is so it would be impossible to address derivation.
 
  • #3
oh lol.. i just found these 2 equations in my textbook and was wondering how is the 2nd equation dervived... anyway thanks for the reply
 
  • #4
The first equation is just pure logic, the total distance traveled by a wave per second is just the number of cycles per second times the wavelength.

The second equation is derived by modelling a medium as a series of discrete particles, then solving the equation of motion of these particles, which can then be used to derive a value for v using the wave equation.

Claude.
 

What is the second equation for wave longitudinal velocity?

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.

How is the second equation derived?

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.

What is the significance of the second equation for wave longitudinal velocity?

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.

Can the second equation be applied to all types of waves?

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.

How does the second equation relate to the first equation for wave velocity?

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.

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