Find wavelength, Phase Difference, and amplitude from min and max

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SUMMARY

The discussion centers on calculating the wavelength, phase difference, and amplitude of sound waves produced by two speakers. The wavelength (λ) is determined to be 80 cm, derived from the relationship that 40 cm corresponds to half of the wavelength. The phase difference (ψ) is calculated to be approximately 37.65 degrees, based on the maximum amplitude condition. The combined amplitude of the two speakers when placed side-by-side is expressed as 2a*cos(Δψ/2), leading to a final amplitude of 0.767a.

PREREQUISITES
  • Understanding of wave mechanics and sound wave properties
  • Familiarity with trigonometric functions and their applications in physics
  • Knowledge of phase difference calculations in wave interference
  • Ability to manipulate equations involving cosine functions
NEXT STEPS
  • Study the principles of wave interference and superposition
  • Learn about the mathematical derivation of phase differences in wave systems
  • Explore the application of trigonometric identities in wave equations
  • Investigate the effects of varying distances between sound sources on amplitude and phase
USEFUL FOR

Students and educators in physics, particularly those focusing on wave mechanics, sound engineering, and acoustics. This discussion is beneficial for anyone seeking to deepen their understanding of wave behavior in multi-source systems.

  • #31
Just had a breakthrough moment. My textbook must be awful because I just understood what these cosine functions are actually representing from your comment and then found an equation that would help.

Amplitude of both = 2a*cos(Δψ/2)

= 2a*cos(1.1775)


Amplitude in terms of a = 0.767a

Submitted, and that was correct.

Thank you both tms and rudeman for your help! I really appreciate you guys and hope one day to give back to the community here at Physics Forums.


Thanks again!
 

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