Sound Waves - phase difference from time delay

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SUMMARY

The discussion focuses on calculating the phase difference between two loudspeakers due to a time delay of 1.56 ms. Given a frequency of 392 Hz and a speed of sound at 340 m/s, the wavelength is determined to be 0.86 m. The phase difference is calculated based on the time delay relative to the period of the wave, which is found to be 2.55 ms. The relationship between time delay and phase difference is crucial for understanding sound wave interactions.

PREREQUISITES
  • Understanding of sound wave properties, including frequency and wavelength.
  • Knowledge of phase difference calculations in wave mechanics.
  • Familiarity with basic trigonometric functions and their application in wave equations.
  • Ability to calculate the period of a wave from its frequency.
NEXT STEPS
  • Study the relationship between time delay and phase difference in wave mechanics.
  • Learn about the mathematical representation of sound waves, specifically using sine functions.
  • Explore the concept of wave interference and its practical applications in acoustics.
  • Investigate the effects of different frequencies on phase differences in sound waves.
USEFUL FOR

Acoustics students, audio engineers, and anyone interested in the physics of sound wave propagation and interference.

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For some reason I have trouble with questions like this. How would I get the phase difference if I were given the time delay of two loudspeakers side by side?

I'll use this question as an example:

"The speakers are now placed side by side. If the wire to speaker 1 is passed through a box that delays the signal by 1.56 ms, what is the new phase difference? "

The frequency is 392 Hz
The PD would be zero since they're beside each other
the speed is 340 m/s
the wavelengths are 0.86 m
and the time delay is 1.56 ms or 1.56e-3 s

I was able to find the period, 2.55e-3 s

But after this I kinda blank out. Any tips?
 
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Think about what the time delay, 1.56 ms means in terms of the period, i.e. what fraction of the period, and how it relates to the wave length.

If one has a signal - A sin[itex]\omega[/itex]t, and another signal of the same form but at a delayed time of td, one could write the delayed signal as A sin[itex]\omega[/itex](t - td).
 

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