In the context of the wave equation, the particle displacement is not directly related to the sound intensity level in decibels (dB). The sound intensity level measures the power of sound waves relative to a reference level and is not directly tied to particle displacement or wavelength.
Particle displacement refers to the distance that particles in a medium (such as air) move from their equilibrium position when a sound wave passes through. The relationship between particle displacement and wavelength depends on the specific characteristics of the wave and the medium.
In a simple harmonic wave, the particle displacement is related to the wavelength (λ) by the equation:
Displacement = A * sin(2πx/λ)
Where:
- Displacement is the particle displacement from the equilibrium position
- A is the amplitude of the wave (related to the sound intensity in a complicated way)
- x is the position along the direction of the wave
However, this equation alone does not allow us to determine the specific intensity level at which the particle displacement is equal to one wavelength. The relationship between particle displacement, wavelength, and sound intensity level requires additional information, such as the amplitude of the wave or the sound pressure level.
If you provide more specific details about the problem or clarify the relationship you're looking for, I can try to help you further.