One violin creates sound of SIL 70 dB

One violin creates sound of SIL 70 dB. Two identical violins will create sound of

The correct answer and explanation is:

Correct Answer: Two identical violins producing sound together will create a sound level of approximately 73 dB.

Explanation:

Decibels (dB) are a logarithmic unit used to measure sound intensity. Because of this logarithmic nature, when you combine two identical sound sources, the increase in decibel level is not a simple addition.

Step 1: Understanding the Decibel Scale

• The decibel scale measures sound intensity relative to a reference level.
• A difference of 10 dB represents a tenfold increase in sound intensity.
• A difference of about 3 dB represents a doubling of the sound intensity (energy).

Step 2: Combining Two Identical Sources

If one violin produces 70 dB, two identical violins will have twice the sound intensity. In decibels, doubling the intensity corresponds to an increase of approximately 3 dB.

So: Total sound level=70 dB+10log⁡10(2)\text{Total sound level} = 70 \text{ dB} + 10 \log_{10}(2)

Since 10log⁡10(2)≈3 dB10 \log_{10}(2) \approx 3 \text{ dB}, Total sound level≈70+3=73 dB\text{Total sound level} \approx 70 + 3 = 73 \text{ dB}

Step 3: Why Not 140 dB?

A common misunderstanding is to add 70 + 70 = 140 dB, but the decibel scale is logarithmic, not linear. A doubling of sound energy adds only 3 dB, not 70.

Additional Notes:

• If you had 4 violins, sound level increases by about 6 dB over one violin (because doubling twice: 3 dB + 3 dB = 6 dB).
• To increase sound level by 10 dB (which sounds roughly twice as loud to human ears), you need 10 times the original intensity.
• The 3 dB rule applies only for sources that are coherent or independent but identical and uncorrelated sources add power, which leads to a 3 dB increase in sound intensity level.

Summary:

Two identical violins each producing 70 dB combined create about 73 dB sound level due to the logarithmic nature of the decibel scale. This increase reflects a doubling of sound energy, not a linear addition of decibel values.