Question on the relationship between intensity of sound, amplitude and 1/r^2

[aznking1]

Homework Statement

Suppose sound wave is emitted uniformly in all directions by a speaker.

At a distance of 1.1m, the amplitude of it sound is 1.2x10^-8m

What is the amplitude of sound at a distance of 1.7m?

The Attempt at a Solution

What I'm confused is why does the amplitude of sound change? Isn't intensity = Power/Area? So at a greater distance, it just means that intensity is lowered. But power from a source is always constant isn't that right? And since power is proportional to amplitude squared, why does the amplitude decrease? am i missing out something?

The answer is 7.8x10^-9 using the relationship of intensity proportional to amplitude^2 and 1/r^2 if you are curious.

 

[mfb]

Isn't intensity = Power/Area? So at a greater distance, it just means that intensity is lowered.

Lower intensity at some specific point corresponds to a lower amplitude at that point. Meters as unit looks odd, I would expect Pa (pressure), but that should be irrelevant.

But power from a source is always constant isn't that right?

Constant in which way? I think you mean the total power here.

 

[aznking1]

Lower intensity at some specific point corresponds to a lower amplitude at that point. Meters as unit looks odd, I would expect Pa (pressure), but that should be irrelevant.

Constant in which way? I think you mean the total power here.

Ahh okay. I think i get it now after reading your post and thinking for so many hours.

Firstly, the formula intensity = power/area gives the power at a particular point. If we were to sum all the points ( surface area of a sphere), we would get the total power of the source, which is always constant

Hence, as distance increases, the intensity at a point decreases, meaning power at the specific point decreases, and so amplitude decreases, as you have mentioned.

Thank you! now i can get a good night's sleep haha... assuming i am correct

 

[mfb]

That is right.
Small issue: "Power at a specific point" is not meaningful. Intensity is. If you integrate that, you get a power.