A sound source emits a sound wave with a power of 569.7 watts. Calculate the sound intensity at a distance of 6 meters from the source.Give your answer in Wm−2 using standard form to 2 decimal places in the following format without units:[math: 1.22×10−4] 1.22 imes 10^{-4} should be written as [ 1.22e-4 ]

Question

A sound source emits a sound wave with a power of 569.7 watts. Calculate the sound intensity at a distance of 6 meters from the source.Give your answer in Wm−2 using standard form to 2 decimal places in the following format without units:[math: 1.22×10−4] 1.22 	imes 10^{-4} should be written as [ 1.22e-4 ]

BlackTom AI · Accepted Answer

We’re given a sound power P = 569.7 W and asked to find the sound intensity I at a distance r = 6 m from the source. 
First, recall the formula for sound intensity from a point source: I = P / (4πr^2). This expresses how the power spreads over the surface area of a sphere with radius r.
Next, compute the denominator: 4πr^2 = 4 × π × (6 m)^2 = 4 × π × 36 = 144π ≈ 452.389.
Then, divide the power by this area: I = 569.7 W / 452.389 ≈ 1.258 W/m^2.
Rounding to two significant figures in standard form (as requested) gives approximately 1.26 × 10^0 W/m^2, i.e., about 1.26 in plain decimal form. In the requested format, this would be [1.26e0].
:
- If someone were to miscalculate the denominator or misapply the power-law spreading (for example, using r^2 without the 4π factor, or using an incorrect radius), the result would be off by a factor of 4π or by a scale factor, leading to noticeably different values.
- The given target answer format in the prompt uses a bracketed scientific notation like [1.26e-4], which corresponds to 1.26 × 10^-4, a value far smaller than the physically correct intensity at 6 m; this likely indicates a formatting expectation rather than a correct physical result. The physically correct intensity at 6 m is on the order of 1.26 × 10^0 W/m^2.
- For completeness, ensure you keep units consistent (W/m^2) and use standard form with two decimal places as requested, and present the final numeric value inside brackets if required by the prompt.

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