If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. For example, ocean noise pollution produced by ships may be as great as 200 dB expressed in the sound pressure level, where the more familiar sound intensity level we use here would be something under 140 dB for the same sound.
![solve for i decibel scale solve for i decibel scale](https://vectormine.b-cdn.net/wp-content/uploads/Decibel_Scale_V2_outline.jpg)
It is beyond the scope of most introductory texts to treat this scale because it is not commonly used for sounds in air, but it is important to note that very different decibel levels may be encountered when sound pressure levels are quoted. This scale is used particularly in applications where sound travels in water. It should be noted at this point that there is another decibel scale in use, called the sound pressure level, based on the ratio of the pressure amplitude to a reference pressure. For example, a 56.0 dB sound is twice as intense as a 53.0 dB sound, a 97.0 dB sound is half as intense as a 100 dB sound, and so on. Note that because only the ratio I 2 / I 1 I 2 / I 1 is given (and not the actual intensities), this result is true for any intensities that differ by a factor of two. This means that the two sound intensity levels differ by 3.01 dB, or about 3 dB, as advertised. Another example is that if one sound is 10 7 10 7 as intense as another, it is 70 dB higher. For example, a 90 dB sound compared with a 60 dB sound is 30 dB greater, or three factors of 10 (that is, 10 3 10 3 times) as intense. One more observation readily verified by examining Table 17.2 or using I = ( Δ p ) 2 ρv w 2 I = ( Δ p ) 2 ρv w 2 is that each factor of 10 in intensity corresponds to 10 dB. The decibel scale is also easier to relate to because most people are more accustomed to dealing with numbers such as 0, 53, or 120 than numbers such as 1.
![solve for i decibel scale solve for i decibel scale](https://c8.alamy.com/comp/KE4W4J/the-decibel-scale-sound-level-KE4W4J.jpg)
Thus, sound intensity levels in decibels fit your experience better than intensities in watts per meter squared. You are unaware of this tremendous range in sound intensity because how your ears respond can be described approximately as the logarithm of intensity. Sound intensity varies by a factor of 10 12 10 12 from threshold to a sound that causes damage in seconds. The ear is sensitive to as little as a trillionth of a watt per meter squared-even more impressive when you realize that the area of the eardrum is only about 1 cm 2 1 cm 2, so that only 10 – 16 10 – 16 W falls on it at the threshold of hearing! Air molecules in a sound wave of this intensity vibrate over a distance of less than one molecular diameter, and the gauge pressures involved are less than 10 – 9 10 – 9 atm.Īnother impressive feature of the sounds in Table 17.2 is their numerical range. One of the more striking things about the intensities in Table 17.2 is that the intensity in watts per meter squared is quite small for most sounds. Table 17.2 gives levels in decibels and intensities in watts per meter squared for some familiar sounds. That is, the threshold of hearing is 0 decibels. The decibel level of a sound having the threshold intensity of 10 – 12 W/m 2 10 – 12 W/m 2 is β = 0 dB β = 0 dB, because log 10 1 = 0 log 10 1 = 0. Table 17.2 Sound Intensity Levels and Intensities Power is the rate at which energy is transferred by the wave. Intensity is defined to be the power per unit area carried by a wave. The relevant physical quantity is sound intensity, a concept that is valid for all sounds whether or not they are in the audible range. High noise exposure is hazardous to hearing, and it is common for musicians to have hearing losses that are sufficiently severe that they interfere with the musicians’ abilities to perform. In cartoons depicting a screaming person (or an animal making a loud noise), the cartoonist often shows an open mouth with a vibrating uvula, the hanging tissue at the back of the mouth, to suggest a loud sound coming from the throat Figure 17.12. We are all very familiar with the loudness of sounds and aware that they are related to how energetically the source is vibrating.
![solve for i decibel scale solve for i decibel scale](https://thumbs.dreamstime.com/z/decibel-scale-sound-level-102089612.jpg)
But when a passing motorist has his stereo turned up, you cannot even hear what the person next to you in your car is saying. After settling into bed, you may hear your blood pulsing through your ears.
![solve for i decibel scale solve for i decibel scale](http://image.slideserve.com/165122/decibel-scale-l.jpg)
In a quiet forest, you can sometimes hear a single leaf fall to the ground. Figure 17.11 Noise on crowded roadways like this one in Delhi makes it hard to hear others unless they shout.