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.

MUF0122 Physics Unit 2 - Semester 2, 2025

View Explanation

Log in for full answers

Similar Questions

If a particular sound S1 is 5 times more intense than another sound S2, then what is the difference in sound intensity levels in dB for these two sounds?

Question at position 10 The unit of measure for the intensity of sound ispitchloudnesshuedecibelsaturation

A sound produced by a speaker has an intensity of 4.2 x 10-6 Wm-2 at a distance of 20 m away.What is its sound intensity level in decibels (dB)?

A loudspeaker emits sound uniformly in all directions with a power output of 1715.8 watts. What is the sound intensity at a distance of 5.3 meters from the loudspeaker?

What is the intensity in watts per meter squared of a 123dB sound? Answer in W/m2. Answer to 1 decimal place and only put in the numerical value. Do not include units in your answer.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler