The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound level goes up by 38.0 dB?
See 6:26 PM post.
To determine the factor by which the amplitude of a sound wave increases when the sound level goes up by 38.0 dB, we can use the formula:
Sound Level (dB) = 10 * log10(I / I₀)
Where:
- Sound Level (dB) is the current sound level
- I is the current intensity of the sound wave
- I₀ is the reference intensity (threshold of hearing), which is 1.0 x 10^(-12) W/m².
We need to find the factor by which the amplitude increases, so we can rewrite the equation as:
I / I₀ = 10^(Sound Level (dB) / 10)
Now, let's calculate the increase in amplitude:
Amplitude Increase Factor = (I₂ / I₁)
Where:
- Amplitude Increase Factor is the factor by which the amplitude increases
- I₂ is the new intensity after the sound level increase
- I₁ is the initial intensity before the sound level increase
Since the amplitude of a sound wave is proportional to the square root of its intensity, we can write:
Amplitude Increase Factor = √(I₂ / I₁)
Now, let's substitute the values into the equation:
Amplitude Increase Factor = √(10^(38.0 / 10))
Calculating this expression, we find:
Amplitude Increase Factor ≈ √(10^3.8)
Amplitude Increase Factor ≈ √(6309.57)
Amplitude Increase Factor ≈ 79.47
Therefore, the amplitude of the sound wave increases by a factor of approximately 79.47 if the sound level goes up by 38.0 dB.
To answer this question, we need to understand how sound levels and amplitudes are related. Sound level is measured in decibels (dB), and it is a logarithmic scale that represents the relative loudness of a sound.
The formula to convert sound levels to amplitudes is given by:
L2 = L1 + 10log(A2/A1)
where L1 and L2 are the initial and final sound levels, and A1 and A2 are the initial and final amplitudes.
In this case, we are given that the sound level increases by 38.0 dB. Let's call the initial sound level L1 and the final sound level L2. Therefore, we have:
L2 = L1 + 38.0 dB
Now, we need to determine the factor by which the amplitude increases. This can be found by rearranging the formula above:
A2/A1 = 10^((L2-L1)/10)
Substituting the values we have:
A2/A1 = 10^((L1+38.0 - L1)/10)
= 10^(38.0/10)
= 10^3.8
Calculating 10^3.8 gives us approximately 6,309.57.
Therefore, the amplitude of a sound wave increases by a factor of approximately 6,309.57 if the sound level goes up by 38.0 dB.