Finding phase difference based on distance

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SUMMARY

The discussion focuses on calculating the phase difference of sound waves generated by a tuning fork at a frequency of 246 Hz in a hall measuring 47.0 m. The user initially calculated the wavelength using the speed of sound (343 m/s) and determined the phase difference based on the distance traveled by the waves. Despite arriving at a phase difference of 144 degrees, the correct answer is 91.3 degrees, attributed to incorrect significant figures in the calculations. The professor confirmed that maintaining five significant figures for distance measurements is essential for accuracy.

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  • Understanding of wave mechanics, specifically phase difference
  • Knowledge of sound wave properties, including frequency and wavelength
  • Familiarity with significant figures in scientific calculations
  • Basic proficiency in trigonometric functions and their applications in physics
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  • Review the principles of wave interference and phase difference calculations
  • Study the relationship between frequency, wavelength, and wave speed in sound
  • Learn about significant figures and their importance in scientific measurements
  • Explore trigonometric identities and their applications in wave physics
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Students studying physics, particularly those focusing on wave mechanics, sound properties, and accurate measurement techniques.

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Homework Statement


A tuning fork is in a hall 47.0 m long, and is placed 14.0 m from one end. It generates a tone of 246Hz. What is the phase difference when the waves traveling in each direction bounce back and meet each other?


Homework Equations


Calculated wavelength with 343/246. Also tried 2pi*38m/1.39m = phi. Also maybe (cos phi/2)sin(kx-omega*t+phi/2)



The Attempt at a Solution



Well, I figured that I could make it simple, calculate the wavelength, divide the difference in distance traveled by wavelengths, getting 27.4 waves, and then multiply .4 * 360 to get things into degrees. This gives me 144 degrees, but the answer in the back of the book is 91.3 degrees. What am I doing wrong?

Thanks in advance.
 
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Had a chance to talk to the prof, and it turns out my method was correct, but my sig figs were off. Apparently, to get a correct answer, it was necessary to assume the distances were correct to about 5 sig figs, even though the book conventionally requires only 3 and the givens were all in 3 sig figs. Poorly written question IMO.
 

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