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If a sound intensity level of 0 dB at 1000 Hz corresponds to a maximum gauge pressure (sound amplitude) of $10^{-9}$ atm, what is the maximum gauge pressure in a $60-dB$ sound? What is the maximum gauge pressure in a $120-dB$ sound?

$p _ { 60 } = 10 ^ { - 6 } \mathrm { atm }$$p _ { 120 } = 10 ^ { - 3 } \mathrm { atm }$

Physics 101 Mechanics

Chapter 17

Physics of Hearing

Sound and Hearing

Cornell University

Simon Fraser University

Hope College

University of Winnipeg

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No. The pressure in pleasure amplitude corresponding to the intensity for zero decibels is given. It is makin bottom Anistan atmospheres. Now, if you remember the intensity off a sound wave is given us p square bye to row. We were released The density off particles We is the velocity off the whale and P is the density and pick you on. The intensity in decibels is given us 10 times locked to the best. And I bite in bar minus reward per meter square. So we use this to right beat Isak Will do, then locked to the best in he's square by two Roby into 10 part minus 12. Now long a baby is long a minus b and lot. So we can like this us locked to the western P square minus lot based. And the rest of it So lock to the based in Peace Square is to lock and to lobby. So that sloppy times 20 Bless I'm sorry. Minus 10 Log Turo, we can for Maestro. We don't care about this. This is static. This is equal nobita. So for our zero decibels, case zero is equal. Do 20 lakh to the best in the P is temper minus nine atmospheres minus. Let's say this whole term is simply some delta, some constant, which does not change. So we want to find the he corresponding to 60 decibels for this for 60 decibels, the corresponding question is 60 is equal to 20. Log to the based in he 60. Let's call this. Let's say this is the pressure intensive pressure amplitude for 60 decibels minus delta. No, it is. If we simply c you can. You can see the Delta from this equation dealt. Isaac will do 20 locked to the West and in bar minus 19 atmosphere. We use that. So this is equal to 20 lakh to the best in pay. 60 minus 20 long to the based in Anbar minus nine atmospheres. I'm sorry too distant, but my last night and that is it. You're there. Well, simply divide by 20 on both sides on. We'll take 10 part on both sides. Notice that the twenties cancelled to give one 60 by 23. So that's 10 cube on the left hand side and on the right hand side. Note. Remember, the temp are a menace. Be eastern body fight and party, so that's in power lock. Lucky Lofty 60. So that's simply P 16 and divided by in power locked to the base. Tintin Bar minus nine is simply tend Bar minus nine. Atmosphere on that is it from this? We see that p sixties equal Do Inbar minus six at most years. No, we'll go to the next part for 1 20 decibels. 1 20 is equal. Do if you remember the previous equation 20 lakh to the best. Um, well, I'll simply call it love from here on 20 lakh p 1 20 minus delta, which is 20. Log in bar minus 19 at most I'm certain about minus nine atmospheres. Now let's go through these steps. It's more slowly so you are clear about it. I'll do it by 20 onboard sites. Excuse us. The question on the left hand side. 1 20 by 26 On the right hand side, the twenties cancer. If you are simply locked to the best in log P 1 20 minus log bottom. Understand atmosphere now Long game Honesty is long. A baby I'm sorry. Log minus log be Is love a divided by be that users log. He won 20 by 10 4 minus nine atmospheres is equal to six. No, because a is equal to be. We know that 10 part A is equal to 10 Barbie it uses 10 past six is equal to 10 part locked to the Weston. He won 20 by in part minus nine atmospheres. Now, if you do remember a to the power off locked to the base Day B is equal to be so using Daddy that identity. We can write this simply as he won 20 right in part minus nine atmospheres. Is it polluted? Bar six. From this equation, we can see that the 1 20 is equal to Kanbar Ministry atmospheres.

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