# Calculating Total Power Output of a Speaker at a Given Distance

• FunkyFrap
In summary, the speaker emits sound waves in all directions with an intensity level of 73 db at a distance of 28 m. To find the total power of the speaker, the equation P=I*A is used, where I is the intensity calculated using I=I_{0}*10^{B/10} and A is the surface area of a sphere with a radius of 28 m. The total power is then calculated to be 0.197 W. There was initial confusion about whether to use the surface area of a sphere or the area of a circle, but it was determined that the original calculation was correct.
FunkyFrap

## Homework Statement

A speaker emits sound waves in all directions, and at a distance of 28 m from it the intensity level is 73 db. What is the total power put out by the speaker, in watts? ( reference intensity $I_{0}$ is 1.0 × 10-12 W/m2.)

## Homework Equations

$P= I*A$
$I = I_{0}*10^{B/10}$
$SA = 4*pi*r^{2}$

## The Attempt at a Solution

Since we're looking for the total power of the speaker, I first used equation 2 to find the intensity, $I$. For $B = 73 db$ and $I_{0} = 10^{-12} W*m^{-2}$ I obtained $I = 2*10^{-5} W*m^{-2}$ .

Then the area is $A = 4*pi*(28)^{2} m^{2} = 9852.03 m^{2}$

Therefore, the total Power is
$P = I*A = 0.197 W$

So that's my attempt but I'm still not entirely confident in that answer. I'm not too sure if the Area equation I'm using is correct. It says in all directions hence why I used surface area but now I'm thinking it's $A = pi*r^2$.

Is that right? Or was the surface area equation the correct one to use?

You were correct in your original calculation. Is there a reason why you were thinking that maybe you should use the area of a circle rather than the surface area of a sphere?

TSny said:
You were correct in your original calculation. Is there a reason why you were thinking that maybe you should use the area of a circle rather than the surface area of a sphere?

I imagined the speaker on the ground, and then imagine the 'sphere' of sound in all directions. I didn't see it as a full sphere, so I thought the first equation wasn't right. Then I guessed it might just be a circle.

OK. Does it make sense now?

TSny said:
OK. Does it make sense now?
Yes it does. Thank you very much!

## 1. What is total power output by a speaker?

Total power output by a speaker refers to the maximum amount of electrical energy that a speaker can convert into sound waves. It is usually measured in watts (W) and is an important factor in determining the loudness and overall audio quality of a speaker.

## 2. How is total power output calculated?

Total power output is calculated by multiplying the voltage and current of the speaker. This is also known as the Watt's Law, which states that power (in watts) is equal to the product of voltage (in volts) and current (in amperes).

## 3. Is higher total power output always better?

Not necessarily. While a higher total power output can result in a louder sound, it does not always guarantee better audio quality. Other factors such as speaker design, frequency response, and driver quality also play a significant role in determining the overall sound performance.

## 4. How does total power output affect speaker efficiency?

The total power output of a speaker is directly related to its efficiency. A higher total power output means the speaker is more efficient at converting electrical energy into sound waves, resulting in a louder and more powerful sound.

## 5. Can total power output be increased?

Total power output can be increased by using an amplifier or by connecting multiple speakers together. However, it is important to note that exceeding the recommended power output of a speaker can damage it and result in poor audio quality.

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