A stereo speaker represented by P in the figure below emits sound waves with a power output of 114 W. What is the intensity of the sound waves at point x when r = 11.8 m?
To find the intensity of the sound waves at point x, we need to use the formula for intensity:
Intensity (I) = Power (P) / Area (A)
Since the stereo speaker emits sound waves evenly in all directions, we can assume that the sound waves spread out in a spherical shape. The area of a sphere is given by the formula:
A = 4πr²
where r is the distance from the source of the waves (in this case, the stereo speaker) to the point where we want to find the intensity.
In this case, r = 11.8 m. So we can calculate the area:
A = 4π(11.8)²
Now, we can calculate the intensity using the given power output:
I = P / A = 114 W / (4π(11.8)²)
To evaluate this expression, we can plug it into a scientific calculator or use numerical approximation techniques.
Therefore, the intensity of the sound waves at point x when r = 11.8 m can be calculated using the formula I = 114 / (4π(11.8)²).