The decibel scale, dB named after inventor Alexander Graham Bell, is also a logarithmic scale, measuring sound levels. The human ear can detect a very wide range of sounds, ranging from a soft whisper to loud machinery. The threshold of pain is about 1120 dB. Examples of other decibel measurements include normal conversation at about 50 dB, and a jet takeoff at about 140 dB The minimum intensity detectable by the human ear is I_(0)=10^-12W/m^2 (watts per square metre)and is used as the reference point.The sound level corresponding to an intensity / watts per square metre is: This formula can also be rewritten as: L=10log(1)/(1_(0)) I=10^(L)/(10)cdot I_(0) 8. Damage to the ear can occur with sound levels that are greater than or equal to 85 dB. Find the sound level of a rock concert with an intensity of 80W/m^2 to determine if fans at the concert are at risk for hearing damage. 9. Normal conversation has a sound level of 60 dB. A night club can have a sound level of 120 dB How many more times intense is the sound level at a night club compared to that normal conversation? 10 The noise in the library is 5000 times less intense than it is in the cafeteria. If the sound level is 80 dB in the cafeteria, what is the sound level in the library?

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The decibel scale, dB named after inventor Alexander Graham Bell, is also a logarithmic scale, measuring sound levels. The human ear can detect a very wide range of sounds, ranging from a soft whisper to loud machinery. The threshold of pain is about 1120 dB. Examples of other decibel measurements include normal conversation at about 50 dB, and a jet takeoff at about 140 dB The minimum intensity detectable by the human ear is I_(0)=10^-12W/m^2 (watts per square metre)and is used as the reference point.The sound level corresponding to an intensity / watts per square metre is: This formula can also be rewritten as: L=10log(1)/(1_(0)) I=10^(L)/(10)cdot I_(0) 8. Damage to the ear can occur with sound levels that are greater than or equal to 85 dB. Find the sound level of a rock concert with an intensity of 80W/m^2 to determine if fans at the concert are at risk for hearing damage. 9. Normal conversation has a sound level of 60 dB. A night club can have a sound level of 120 dB How many more times intense is the sound level at a night club compared to that normal conversation? 10 The noise in the library is 5000 times less intense than it is in the cafeteria. If the sound level is 80 dB in the cafeteria, what is the sound level in the library?

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8. We are given the intensity, *I*, of the rock concert as 80 W/m² and the reference intensity *I₀* as 10⁻¹² W/m². We can use the formula *L* = 10log(*I*/*I₀*) to find the sound level. *L* = 10log(80 / 10⁻¹²) *L* = 10log(8 x 10¹³) *L* ≈ 10 * (13.9) *L* ≈ 139 dB Since 139 dB is greater than 85 dB, fans at the concert *are* at risk for hearing damage. 9. Let *I₁* be the intensity of normal conversation (60 dB) and *I₂* be the intensity of the nightclub (120 dB). We can use the formula *I* = 10^(*/L*/¹⁰) * *I₀*. *I₁* = 10⁶ * *I₀* *I₂* = 10¹² * *I₀* To find how many times more intense the nightclub is, we divide *I₂* by *I₁*: *I₂* / *I₁* = (10¹² * *I₀*) / (10⁶ * *I₀*) = 10⁶ The sound level at a nightclub is 1,000,000 (one million) times more intense than a normal conversation. 10. Let *I₁* be the intensity in the library and *I₂* be the intensity in the cafeteria (80 dB). We are given that *I₁* = *I₂* / 5000. We first find *I₂* using the formula *I* = 10^(*/L*/¹⁰) * *I₀*: *I₂* = 10⁸ * *I₀* Now we can find *I₁*: *I₁* = (10⁸ * *I₀*) / 5000 = (10⁸ / 5 x 10³) * *I₀* = 2 x 10⁴ * *I₀* Now we can find the sound level in the library (*L₁*) using the formula *L* = 10log(*I*/*I₀*): *L₁* = 10log((2 x 10⁴ * *I₀*) / *I₀*) *L₁* = 10log(2 x 10⁴) *L₁* ≈ 10 * 4.3 *L₁* ≈ 43 dB The sound level in the library is approximately 43 dB.

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