Jet Engines and Decibels

I’m taking a class on drawing and one student drew two men talking behind two jet engines.

Elizabeth commented, “on a practical note, how’s he going to hear the fellow behind him? Protective ear gear, not looking at each other, an approximate 130db noise level from the engine…”

Tim replied, “They have wireless y’know. And anyway there’s two engines so that’d be 260dB!”

My response:

Cool drawings, might have to correct your acoustics statement though.

Two engines at 130 dB does not equal 260 dB. If we assume that each engine generates 130 dB, it would be more like 133 dB for two engines.

Decibels are not a linear system. It’s more like the Richter scale for earthquakes. That allows our ears to hear a greater range of intensity.

Let’s say we have one saxophone playing something compared to 10 saxophones playing that same thing in unison.

Then 10 saxophones in unison would sound twice as loud as the one saxophone.

dB level = 10 log(I/I0)

Where I0 is generally the threshold of hearing for humans.

Using a property of logs (a is the base, ten in this case)

loga (xy) = loga x + loga y

If you double the intensity, then you add 10log(2) to the original dB level. That means adding about 3 dB to the original 130 dB to get 133 dB. (That’s if the two engines are in unison)

Elizabeth saying approximately 130 dB is actually fairly accurate.

Study Guide for the Final

Problems to focus on:

Chapter 26: 5, 20, 27, 30, 42, 51

Chapter 27:  1, 16 (and stationary observer variation), 20, 31, 36

Chapter 28: 8, 9, 13, 35, 40

Chapter 29: 40

Chapter 30: 5, 25


Notes: You may bring one side of an 8.5 x 11 sheet of paper with equations.  Don’t put examples on it.


Topics may include:

RMS current and voltage, power use, impedance, RLC circuits, relative motion, relativistic effects, length contraction, time dilation, the photoelectric effect, particle in a box, absorption and emission, binding energy, radioactive decay and half lives.

Assignment #12 – Chapter 27 Problems

Chapter 27

1*, 4, 7, 8, 12, 15, 16, 20, 21, 28, 31, 36

Due Monday

For problem 1, modify it so that the sound appears to be traveling at 335 m/s and 355 m/s.  The numbers listed seem fishy though.

One source stated Usain Bolt’s top speed was 43.93 km/h ( 27.3 mph) in m/s is 12.2 m/s.

I used 12 m/s as an approximation for his max speed.

If you used the numbers listed in the book…… you would get a speed that seems unreasonable to me.