If the energy carried by a sound wave is multiplied by a thousand, by what factor does the intensity of the sound wave increase?
Since this is not my area of expertise, I searched Google under the key words "sound wave loudness" to get this source:
http://www.newi.ac.uk/buckleyc/sound.htm
"The loudness of sound is largely subjective, the ticking of an alarm which is perceived as quiet during the day can seem annoyingly loud during the night as can a distant burglar alarm even though in reality the "noise" is small. Loudness is measured in decibels (dB) which is the ratio of the intensity of the sound to that of a standard sound of 0.000 000 000 001 watts/sq.metre at 1000 Hz which is just about the faintest sound that a typical young person can hear. A sound ten times as intense as this standard sound is rated at 10 dB or 1 B (Bel). The decibel scale is a logarithmic scale thus 11 dB is 10 times more intense that 10 dB and 15 dB is 100 000 times more intense than 10 dB."
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
To determine the factor by which the intensity of a sound wave increases when the energy carried by it is multiplied by a thousand, we need to understand the relationship between energy and intensity.
Intensity (I) is defined as the amount of power (P) transferred through an area (A) perpendicular to the direction of the wave propagation. Mathematically, it can be expressed as:
I = P/A
The power (P) of a sound wave is directly proportional to the energy (E) carried by the wave. Therefore, we can represent the relationship as:
P ∝ E
When the energy (E) is multiplied by a factor of one thousand, the power (P) also gets multiplied by one thousand. So, we can express it as:
P' = 1000P
Now, let's consider that the area (A) remains constant. Combining the above equations, we get:
I' = P'/A = 1000P/A = 1000I
Therefore, when the energy carried by a sound wave is multiplied by a thousand, the intensity of the sound wave increases by a factor of one thousand.