Day 19

Thursday, April 13, 2017

7.3 Vibrating rectangular membrane, cont'd

20170406_080600_rectangular_membrane_pickup_math_bldg.jpg 2017_04_06/20170406_135623.jpg

L = 2. M=2, n=2, m=1 mode of square membrane


Note: if the above image is not animated, try Firefox. Chrome does not yet support animated pngs.

(Code that made above animation:

Frequencies of rectangular membrane as a function of H/L

The "spectrum" of the solutions, i.e. the set of (square-roots of) the eigenvalues, is to a large extent what gives each object it's characteristic sound.

mystery object 1

mystery object 2

mystery object 3

2017_04_13/20170413_135226.jpg 2017_04_13/20170413_135240.jpg

(Code that made above plot:

Let us examine the spectrum of the square membrane.

virtual piano

2017_04_13/20170413_135300.jpg lowest_7_freqs_rect_membrane.ipynb.png 2017_04_13/20170413_135308.jpg 2_2_and_4_1_onL2H1.png

Vibrating circular membrane (e.g. drum head)

We will also look at vibrating circular membranes, such as:

kick_drum.jpg eardrum.jpg