Equation of variation of displacement and pressure of sound wave

In summary, the two books have different equations for the graph of pressure in sound waves, with one book showing p=p max sin (wt-kx-(pi/2)) and the other showing p=p max sin (wt-kx+(pi/2)). The correct equation is unclear, but one book also includes a phasor diagram showing displacement leading, while the other book does not mention this. The displacement may be leading in the equation shown, but it is not explicitly stated.
  • #1
kelvin macks
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0

Homework Statement



i have attached the notes from 2 books below, i know that the graph of pressure of sound waves lag behind the displacement grpah by 90 degree. so it should be p=p max sin (wt-kx-(pi/2)) am i right? why the another book gives p=p max sin (wt-kx+(pi/2)) ? which is correct? the second and third photo are from the same book.

Homework Equations





The Attempt at a Solution

 

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  • #2
No, I think p=p max sin (wt-kx+(pi/2)) is right. Either that or p=p max sin (-wt+kx-(pi/2)). And I wouldn't describe that as lagging behind. I think the displacement is the one that's lagging.
 
  • #3
dauto said:
No, I think p=p max sin (wt-kx+(pi/2)) is right. Either that or p=p max sin (-wt+kx-(pi/2)). And I wouldn't describe that as lagging behind. I think the displacement is the one that's lagging.

why do u say displacement is the one that's lagging ? i have drawn the phasor diagram at t=o. it shows that dispacement is leading am i right?
 

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Last edited:

What is the equation of variation of displacement and pressure of a sound wave?

The equation of variation of displacement and pressure of a sound wave is given by the wave equation, which is represented as y(x,t) = A sin(kx - ωt) where y(x,t) is the displacement of the wave at position x and time t, A is the amplitude of the wave, k is the wave number, and ω is the angular frequency.

What is the relationship between displacement and pressure in a sound wave?

In a sound wave, displacement and pressure are directly proportional to each other. This means that as the displacement of the wave increases, the pressure also increases, and vice versa. This relationship is described by the equation P = ρc²y, where P is the pressure, ρ is the density of the medium, c is the speed of sound, and y is the displacement.

How does the equation of variation of displacement and pressure change in different mediums?

The equation of variation of displacement and pressure of a sound wave remains the same in different mediums, as long as the medium is linear and homogeneous. However, the values of A, k, and ω may change depending on the properties of the medium, such as density and elasticity.

Can the equation of variation of displacement and pressure be used for all types of sound waves?

The equation of variation of displacement and pressure can be used for all types of sound waves, as long as the waves are longitudinal and travel through a medium. This includes both audible and inaudible sound waves, such as ultrasound and infrasound.

How is the equation of variation of displacement and pressure derived?

The equation of variation of displacement and pressure is derived from the wave equation, which is a mathematical model that describes the behavior of waves. It takes into account the properties of the medium, such as density and elasticity, and the motion of the wave, represented by the sine function. By applying the wave equation to the specific case of sound waves, we can derive the equation of variation of displacement and pressure.

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