Intensity of sound wave when given sound intensity level.

In summary, the conversation discusses how to calculate the intensity of a sound wave with a sound intensity level of 34 dB, using the equation B = (10dB) log (I/Io). The attempt at a solution involves rearranging the equation and plugging in values, but the result is incorrect. After seeking help, it is discovered that the error was due to a miscalculation of 10^3.4. The correct intensity is 2.0x10^-9 W/m^2.
  • #1
Ericv_91
25
1

Homework Statement



What is the intensity of sound wave with sound intensity level 34 dB?


Homework Equations



B = (10dB) log (I/Io) B = sound intensity level, I = intensity, Io= 1.0x10^-12 W/m^2



The Attempt at a Solution



I figured it would be simply a matter of rearranging the equation above to solve for I and entering all the values giving:

I = Io x 10^(B/10 dB)
I = (1.0x10^-12) x 10^(34/10)
I = 2.0x10^-9 W/m^2

However the assignment tells me that I am wrong. Am I missing something very very basic? Am I using the wrong equation all together? My textbook won't tell me, so I've turned to Physics Forums. :uhh:
 
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  • #2
Recalculate 10^3.4.

ehild
 
  • #3
My calculator decided to cut off a 5 after the 2. *sigh*. Thanks.
 

1. What is the difference between sound intensity level and intensity of a sound wave?

Sound intensity level is a measure of the magnitude of sound waves, expressed in decibels (dB). It is a logarithmic scale that compares the intensity of a sound wave to a reference intensity. Intensity of a sound wave, on the other hand, is a physical quantity that represents the amount of energy carried by the sound wave per unit area. It is measured in watts per square meter (W/m^2).

2. How is sound intensity level calculated?

Sound intensity level (SIL) is calculated using the formula SIL = 10log(I/I0), where I is the intensity of the sound wave and I0 is the reference intensity. The reference intensity is typically set at 10^-12 W/m^2, which is the threshold of human hearing. This formula shows that sound intensity level is directly proportional to the logarithm of sound intensity.

3. Can sound intensity level and intensity of a sound wave be measured directly?

No, sound intensity level and intensity of a sound wave cannot be measured directly. These quantities are calculated using specialized instruments such as sound level meters and acoustic intensity probes. These instruments measure the sound pressure level and sound intensity, respectively, and then use the appropriate formulas to calculate the intensity level and intensity of the sound wave.

4. How does the distance from the sound source affect the intensity of a sound wave?

The intensity of a sound wave decreases as the distance from the source increases. This is because the energy of the sound wave is spread out over a larger area, resulting in a lower intensity. The relationship between distance and intensity is inverse-square, meaning that the intensity decreases by a factor of four when the distance is doubled. This is known as the inverse-square law of sound propagation.

5. What are some real-world applications of understanding sound intensity level and intensity of sound waves?

Understanding sound intensity level and intensity of sound waves is crucial in many real-world applications. For example, in the field of occupational health and safety, it is important to measure and control sound levels in workplaces to prevent hearing loss. In music and audio engineering, knowledge of sound intensity and intensity level is essential for creating and mixing high-quality sound. Additionally, understanding these concepts is important in fields such as ultrasound imaging, noise control, and sonar technology.

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