Equation of variation of displacement and pressure of sound wave

Click For Summary
SUMMARY

The discussion centers on the equations representing the relationship between displacement and pressure in sound waves. The correct equation for pressure is confirmed as p = p_max sin(wt - kx + (π/2)), indicating that displacement leads pressure by 90 degrees. The confusion arises from differing interpretations of phase relationships, with one participant asserting that displacement lags behind pressure, which is incorrect. The phasor diagram drawn at t=0 supports the conclusion that displacement indeed leads pressure.

PREREQUISITES
  • Understanding of wave mechanics and sound wave properties
  • Familiarity with sinusoidal functions and phase shifts
  • Knowledge of phasor diagrams and their applications in wave analysis
  • Basic grasp of trigonometric identities and their relevance in physics
NEXT STEPS
  • Study the derivation of wave equations in acoustics
  • Learn about phase relationships in harmonic motion
  • Explore the application of phasor diagrams in analyzing wave phenomena
  • Investigate the mathematical representation of sound waves in different media
USEFUL FOR

Students and educators in physics, particularly those focusing on wave mechanics, sound engineering professionals, and anyone interested in the mathematical modeling of sound waves.

kelvin macks
Messages
60
Reaction score
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

 

Attachments

  • IMG_20140606_083900[1].jpg
    IMG_20140606_083900[1].jpg
    59.4 KB · Views: 613
  • IMG_20140606_084405[1].jpg
    IMG_20140606_084405[1].jpg
    28.7 KB · Views: 670
  • IMG_20140606_084232.jpg
    IMG_20140606_084232.jpg
    74.9 KB · Views: 1,071
Physics news on Phys.org
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.
 
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?
 

Attachments

  • IMG_20140607_071953[1].jpg
    IMG_20140607_071953[1].jpg
    38.8 KB · Views: 541
Last edited:

Similar threads

Is Reflection of an Incident Wave Lagging or Advancing?
  • · Replies 1 ·
Replies
1
Views
1K
Wave function - displacement - transverse wave
  • · Replies 3 ·
Replies
3
Views
2K
Max velocity of a vibrating loud speaker membrane given sound intensity
  • · Replies 4 ·
Replies
4
Views
2K
Contradiction in Phase of reflected sound
  • · Replies 1 ·
Replies
1
Views
1K
Traveling and Standing Wave Equations
  • · Replies 10 ·
Replies
10
Views
8K
The longitudinal displacement of sound wave
  • · Replies 1 ·
Replies
1
Views
4K
Understanding MIT's applet on sound with Fourier coefficients
  • · Replies 3 ·
Replies
3
Views
1K
Pressure Variance, Displacement, and a Soft Drink Bottle
  • · Replies 11 ·
Replies
11
Views
3K
Uncertainties For Wave Packets
  • · Replies 4 ·
Replies
4
Views
1K
Sound Wave Interference and Finding the Path Differences with Diagrams
  • · Replies 20 ·
Replies
20
Views
5K