If the amplitude of a sound wave is tripled,
A.) by what factor will the intensity increase?
B.) by how many dB will the sound level increase?
A.) The intensity of a sound wave is directly proportional to the square of its amplitude. Therefore, if the amplitude of a sound wave is tripled, the intensity will increase by a factor of (3)^2 = 9.
B.) The sound level in decibels (dB) is given by the formula:
L = 10 log10(I/I0)
where I is the intensity of the sound wave and I0 is the reference intensity (typically the threshold of human hearing, which is approximately 10^-12 watts per square meter).
If the amplitude is tripled, the intensity increases by a factor of 9, as found in part A. Therefore, the sound level will increase by 10 log10(9) = 10 × 0.954 = 9.54 dB.
To determine the answers to these questions, we need to understand the relationships between amplitude, intensity, and sound level.
Amplitude refers to the maximum displacement of particles in a medium caused by a sound wave. It determines the "loudness" or strength of the sound.
Intensity is a measure of the amount of energy transported by the sound wave per unit of area perpendicular to the direction of the sound wave's propagation. It is directly proportional to the square of the amplitude.
Sound level, on the other hand, is a logarithmic measurement of the intensity relative to a reference level. It is measured in decibels (dB).
Now let's answer the questions step by step:
A.) If the amplitude of a sound wave is tripled, the intensity will increase by a factor of 9. This is because intensity is proportional to the square of the amplitude. So, if the amplitude is increased by a factor of 3, the intensity will increase by (3^2) = 9 times.
B.) To calculate the increase in sound level in decibels (dB), we can use the formula:
ΔL = 10 * log10(I2/I1),
where ΔL is the change in sound level, I2 is the final intensity, and I1 is the initial intensity.
Since the intensity increases by a factor of 9 (as determined in A.), the ratio I2/I1 is equal to 9. Plugging this into the formula:
ΔL = 10 * log10(9) ≈ 10 * 0.9542 ≈ 9.542 dB.
Therefore, the sound level will increase by approximately 9.542 dB.
To summarize:
A.) The intensity will increase by a factor of 9.
B.) The sound level will increase by approximately 9.542 dB.
A) 3^2 = 9
Intensity is proportional to the square of ampltitude.
B) I2/I1 = 9
dB = 10 Log(I/Io)
dB2 - dB1 = 10 Log(I2/I1)= 10 Log9 = 9.5