Change in sound intensity over distance

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SUMMARY

The discussion focuses on calculating sound intensity changes from two trains emitting sound at 440 Hz, one approaching and one receding at a speed of 11 m/s. The intensity formula I = P/(4πr²) is utilized to determine the time for the approaching train's sound intensity to increase by 2 dB and the distance of the receding train when its intensity decreases by 6 dB. Key equations include dB = 10 log(I/I0) and the relationship between intensity and distance. The velocity of sound in air is given as 343 m/s.

PREREQUISITES
  • Understanding of sound intensity and decibel calculations
  • Familiarity with the inverse square law for sound
  • Knowledge of basic physics concepts related to motion and sound
  • Ability to manipulate logarithmic equations
NEXT STEPS
  • Study the relationship between sound intensity and distance using the inverse square law
  • Learn how to convert between intensity and decibels using logarithmic functions
  • Explore the Doppler effect and its impact on sound frequency and intensity
  • Investigate practical applications of sound intensity calculations in acoustics
USEFUL FOR

Students studying physics, particularly those focusing on acoustics and sound wave behavior, as well as educators seeking to explain sound intensity concepts in real-world scenarios.

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Homework Statement


You are standing in between two sets of railroad tracks. On one set of tracks a train is initially 200 m away and approaching you with a constant speed of v0 = 11 m/s. On the other set of tracks second train is at the same distance and moving away from you at the same constant velocity. Both trains are blowing their horns. The output power of each horn is the same and the frequency of each horn is 440 Hz. Take the velocity of sound in air to be vair = 343 m/s.

Calculate the time it will take for the sound intensity from the approaching train at your position to increase by 2 dB?

Calculate the distance of the receding train from your position when its sound intensity has decreased by 6 dB?

Homework Equations


I=P/4πr2
dB=10log(I/I0)

The Attempt at a Solution


Not really sure where to start, I do not know how to get dB into power so that I can use the first equation. Once I find the distance I know how to find the time, but I am having trouble relating distance to change in decibels.
 
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Start with I(r) = P_o/4∏r^2

I0 = I_o = I(r_o) = P_o/4∏r_o^2

now use dB=10log(I/I0)

?
 

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