Question about Sound an intensiy

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To determine the distance required to hear a 4000Hz sound at the same perceived loudness as a 500Hz sound at 1.0m, the intensity of the 4000Hz sound must first be calculated, as intensity is proportional to the square of the frequency. The initial intensity of the 500Hz sound is given as 4.0x10^-4 W/m². Using the inverse square law, the distance can then be found by setting the intensity of the 4000Hz sound equal to 4.0x10^-4 W/m². The discussion highlights confusion regarding the calculation of distances, emphasizing the need for clarity in applying the formulas correctly. Ultimately, understanding the relationship between frequency, intensity, and distance is crucial for solving the problem accurately.
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Homework Statement



A speaker delivers 500Hz sound at an intensity of 4.0x10^-4 W/m² when measured at a distance of 1.0m from the speaker. At what distance from the speaker would you have to be to hear 4000Hz sound at the same perceived loudness?


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The Attempt at a Solution



I keep getting very short distances that do not make sense. If i could get some help on how to start this it would be great.
 
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Intensity is proportional to the square of frequency. So find the intensity at 1m due to the source of 4000 Hz. Then using inverse square law find the distance where the intensity well be 4x10^-4 W/m^2
 
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