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How many times greater is the intensity of sound from a concert speaker at a distance of 35 meters than the intensity at a distance of 175 meters?

Ask by Parsons Elliott. in the United States
Mar 12,2025

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The intensity of sound at 35 meters is 25 times greater than at 175 meters.

Solución

1. The intensity \( I \) of sound from a point source is inversely proportional to the square of the distance \( r \) from the source: \[ I \propto \frac{1}{r^2} \] 2. Let \( I_{35} \) be the intensity at \( r = 35 \) meters and \( I_{175} \) be the intensity at \( r = 175 \) meters. We have: \[ I_{35} \propto \frac{1}{35^2} \quad \text{and} \quad I_{175} \propto \frac{1}{175^2} \] 3. The ratio of the intensities is: \[ \frac{I_{35}}{I_{175}} = \frac{\frac{1}{35^2}}{\frac{1}{175^2}} = \frac{175^2}{35^2} \] 4. Notice that: \[ \frac{175}{35} = 5 \quad \text{so} \quad \frac{175^2}{35^2} = 5^2 = 25 \] 5. Therefore, the intensity at 35 meters is 25 times greater than the intensity at 175 meters: \[ I_{35} = 25 \, I_{175} \]

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The intensity of sound decreases with the square of the distance from the source, following the inverse square law. If you have a concert speaker, and you compare the sound intensity at 35 meters to that at 175 meters, you can set up the ratio. The distance factor is 175/35, which is 5. Since the intensity is inversely proportional to the square of the distance, you'll calculate: Intensity Ratio = (Distance1/Distance2)² = (175/35)² = 5² = 25. So, the intensity of sound from the concert speaker at 35 meters is 25 times greater than at 175 meters. Now, to keep the excitement going! Ever been to a concert and wondered why you can feel those bass beats from the front row but not so much from the back? That's all about intensity and how sound travels! The closer you are to the source, the more power those vibrations pack! Want to dive deeper into sound? Check out concepts like decibels and how sound waves are manipulated in different environments, or consider exploring how acoustics impact music venues—it's a whole science unto itself! You'll find tons of fascinating material on the interplay between sound and space!

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