-
Notifications
You must be signed in to change notification settings - Fork 1
Expand file tree
/
Copy paththeory.html
More file actions
383 lines (285 loc) · 14 KB
/
Copy paththeory.html
File metadata and controls
383 lines (285 loc) · 14 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
<title>Online Tone Generator 2.0 - A simple, easy and accurate explanation of the decibel.</title>
<meta name="viewport" content="initial-scale=1">
<script async src="https://cdn.fuseplatform.net/publift/tags/2/3547/fuse.js"></script>
<link rel="shortcut icon" type="image/png" href="favicon.png">
<link href="css/main.css" rel="stylesheet" type="text/css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.6.1/jquery.min.js"></script>
<script async src="https://www.googletagmanager.com/gtag/js?id=G-Z8TTZXQT2S"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());
gtag('config', 'G-Z8TTZXQT2S');
</script>
<style>
/* Styles for publift */
body {
margin-bottom:100px;
}
#wrapper {
max-width: 1100px;
}
@media only screen and (max-width: 1868px) {
.fuse-sidebar {
width:160px!important;
}
}
@media only screen and (max-width: 1700px) {
.fuse-sidebar {
width:160px!important;
}
#wrapper {
max-width: 1000px;
}
}
@media only screen and (max-width: 1423px) {
#wrapper {
max-width: 1100px;
}
.fuse-sidebar {
display:none!important;
}
}
</style>
</head>
<body class="">
<div class="site-outer-wrapper" style="max-width: 1900px;margin: 0 auto;text-align:center;">
<div class="fuse-sidebar" style="width:200px;float:left;width: 300px;position: sticky;top:20px;margin:20px;display:inline-block;">
<div data-fuse="23080447251"></div>
</div>
<div id="wrapper" style="display: inline-block;text-align:left;">
<div id="navMenu">
<ul id="nav" class=''>
<li><a href="theory.html#" class="js-menu-toggle">☰ Show menu</a></li>
<li>
<a class="" href="index.html">Home </a>
</li>
<li>
<a class="" href="multiple-tone-generator.html">Multiple Tone Generator </a>
</li>
<li>
<a class="" href="pitch-shifter.html">Pitch Shifter </a>
</li>
<li>
<a class="" href="time-stretcher.html">Time Stretcher </a>
</li>
<li>
<a class="" href="voice-generator.html">Voice Generator </a>
</li>
<li>
<a class="" href="voice-recorder.html">Voice Recorder <span class="new">NEW</span></a>
</li>
<li>
<a class="" href="frequency-sweep-generator.html">Sweep Generator </a>
</li>
<li>
<a class="" href="tuning.html">Instrument Tuning </a>
</li>
<li>
<a class="" href="subwoofer.html">Subwoofer Testing </a>
</li>
<li>
<a class="" href="hearingtest.html">Hearing Test </a>
</li>
<li>
<a class="" href="noise.html">Noise Generator </a>
</li>
<li>
<a class="" href="binauralbeats.html">Binaural Beats </a>
</li>
<li>
<a class="" href="432Hz.html">432Hz Frequency </a>
</li>
<li>
<a class="" href="dtmf.html">DTMF Signals </a>
</li>
<li>
<a class="" href="metronome.html">Metronome </a>
</li>
<li>
<a class="" href="pips.html">The Pips </a>
</li>
<li>
<a class="current" href="theory.html">Acoustic Theory </a>
</li>
<li class="">
<a class="" href="shop.html">Shop <span class="new">NEW</span></a>
</li>
<li class="">
<a class="" href="about.html">About </a>
</li>
<li>
<a target="_blank" rel="noreferrer" href="https://ko-fi.com/onlinetonegenerator" class="last">Support the developer <span style="font-family:sans-serif;">☕</span></a>
</li>
</ul>
<!-- <div style="padding:8px;" class="iframe-wrapper">
<p style="margin-top:0px;font-size: 13px;">
Visit our partner site <a href="https://digitalpiano.app/" target="_blank">Digital Piano App</a></p>
<a href="https://digitalpiano.app/" target="_blank"><img style="width:100%;border: 1px solid #CCC;" src="https://digitalpiano.app/DPA-social-media-tile.png"></a>
</div> -->
<!-- <div class="iframe-wrapper" id='amazon-wrapper'>
<iframe style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src=''></iframe>
</div> -->
<script>
// $("#amazon-wrapper iframe").attr("src", function(){
// var srcs = ["//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=onlitonegene-20&marketplace=amazon®ion=US&placement=B00K6CX3MO&asins=B00K6CX3MO&linkId=NEWHD3WDVKT2VKR5&show_border=true&link_opens_in_new_window=true&price_color=27A159&title_color=0066C0&bg_color=FFFFFF",
// "//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=onlitonegene-20&marketplace=amazon®ion=US&placement=B004M8UZS8&asins=B004M8UZS8&linkId=UA3S6OIXAOJMPH3F&show_border=true&link_opens_in_new_window=true&price_color=27A159&title_color=0066C0&bg_color=FFFFFF",
// "//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=onlitonegene-20&marketplace=amazon®ion=US&placement=B00WK47VEW&asins=B00WK47VEW&linkId=7LEBKY765ADLYRNI&show_border=true&link_opens_in_new_window=true&price_color=27A159&title_color=0066C0&bg_color=FFFFFF",
// "//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=onlitonegene-20&marketplace=amazon®ion=US&placement=B0070U8KSM&asins=B0070U8KSM&linkId=KMSKNV3B2EYCNTIX&show_border=true&link_opens_in_new_window=true&&price_color=27A159&title_color=0066C0&bg_color=FFFFFF",
// "//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=onlitonegene-20&marketplace=amazon®ion=US&placement=B006HCQZDQ&asins=B006HCQZDQ&linkId=XE56EMXTDCCJHNQQ&show_border=true&link_opens_in_new_window=true&price_color=27A159&title_color=0066C0&bg_color=FFFFFF",
// "//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=onlitonegene-20&marketplace=amazon®ion=US&placement=B00B5SKWBS&asins=B00B5SKWBS&linkId=PIY74OWTXMFMWMC4&show_border=true&link_opens_in_new_window=true&price_color=27A159&title_color=0066C0&bg_color=FFFFFF"
// ]
// var min = 0;
// var max = srcs.length - 1;
// var rand = Math.floor(Math.random()*(max-min+1)+min);
// return srcs[rand];
// });
$(".js-menu-toggle").click(function(e){
e.preventDefault();
$nav = $(this).parents("#nav");
if ($nav.hasClass("js-open")){
// $nav.height($(this).outerHeight());
$(this).html("☰ Show menu");
} else {
// $nav.height("auto");
$(this).html("☰ Close menu");
}
$nav.toggleClass("js-open");
});
</script>
</div>
<div id="mainContent">
<h1><a href='index.html'><!-- <img src="/img/Speaker_Icon-tilted.png" alt=""> -->Online Tone Generator 2.0</a></h1>
<p class="tagline"><strong>What is a decibel?</strong></p>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<div id="theory">
<p>
The internet is full of overly complicated explanations of this widely used but rarely understood unit of measurement.
</p>
<p>
Firstly, it is important to understand <em>exponents</em> and <em>logarithms</em>. Here's a simple example:
\[ 100 = 10^2 = 10\times10 \]
Here, the little 2 is called the <em>exponent</em>. It means multiply 10 by itself twice. Similarly, for:
\[ 1000 = 10^3 = 10\times10\times10 \]
3 is the exponent, and means multiply 10 by itself 3 times.
</p>
<div class="fuse-in-content" style="margin:20px 0;min-height: 250px;max-width:100%;">
<!-- GAM 71161633/OLGEN_onlinetonegenerator/incontent_1 -->
<div data-fuse="23080803961"></div>
</div>
<p>
A <em>logarithm</em> is the exact opposite of an exponent. Take another simple example.
This is pronounced "the logarithm to base ten of one thousand equals three":
\[ \log_{10} 1000 = 3 \]
10 is called the <em>base</em>. The logarithm of 1000 is simply the number of times
the base (in this case 10) must be multiplied by itself to get to 1000, i.e. 3 times.
And you should notice that this is just the same as the exponent from the equation above.
Each equation uses the same three numbers, just arranged in a slightly different way.
</p>
<p>
Now, the strange thing is that exponents and bases don't have to be whole numbers.
In fact, they can be any numbers at all. Here is a completely random example:
\[ 6^{4.7} = 4542.6674 \]
\[ \log_{6} 4542.6674 = 4.7 \]
One important rule to learn is that the logarithm of 1 is always zero, regardless of its base.
</p>
<div class="fuse-in-content" style="margin:20px 0;min-height: 250px;max-width: 100%;">
<!-- GAM 71161633/OLGEN_onlinetonegenerator/incontent_2 -->
<div data-fuse="23081403308"></div>
</div>
<h3>The decibel</h3>
<p>
The <em>decibel</em> (dB) is one tenth of a <em>bel</em> and is named in honour of
<a href="https://en.wikipedia.org/wiki/Alexander_Graham_Bell" title="Alexander Graham Bell" target="_blank">Alexander Graham Bell</a>.
The intensity in dB of a sound of intensity I is given by
\[ I(dB) = 10\log_{10}\left[\frac{I}{I_0}\right] \]
It is a <em>relative</em> unit which means it only makes sense when you have a reference level to compare to.
For our reference we use the threshold of human hearing. The quietest thing any human can hear,
I<span class="superscript">0</span>, is one trillionth of a watt per square meter. So, if a sound is
twice as intense as I<span class="superscript">0</span>, its intensity will be
\[ 10\log_{10} \left[\frac{2I_0}{I_0}\right] = 10\log_{10}2 = 3 dB \]
</p>
<!--<p>Sound is often measured as power which is the square of intensity. The following table contains a list of the intensities and dB levels of some common scenarios.</p>-->
<table id="dBTable">
<tr>
<th>Scenario</th>
<th>Number of times more intense than I<span class="superscript">0</span></th>
<th>Intensity in dB</th>
</tr>
<tr>
<td>Limit of human hearing</td>
<td>1</td>
<td>0</td>
</tr>
<tr>
<td>Sound of Breathing</td>
<td>10</td>
<td>10</td>
</tr>
<tr>
<td>Whispering</td>
<td>100</td>
<td>20</td>
</tr>
<tr>
<td>Loud Conversation</td>
<td>100,000</td>
<td>50</td>
</tr>
<tr>
<td>Busy Street</td>
<td>10,000,000</td>
<td>70</td>
</tr>
<tr>
<td>Thunder</td>
<td>10,000,000,000</td>
<td>100</td>
</tr>
<tr>
<td>Jet Plane on Take-off</td>
<td>100,000,000,000,000</td>
<td>140</td>
</tr>
<tr>
<td>Space Rocket Launch</td>
<td>10,000,000,000,000,000,000</td>
<td>190</td>
</tr>
</table>
</div>
</div>
<div id="footer">
Online Tone Generator utilises HTML5 and the Web Audio API. It is optimized for use with the latest versions of Chrome, Safari, Firefox and Microsoft Edge.
<br />
© onlinetonegenerator.github.io <a href="privacy-policy.html">Privacy Policy.</a>
</div>
</div><!-- End of main content wrapper -->
<div class="fuse-sidebar" style="display:inline-block;vertical-align:top;width: 300px;position: sticky;top:20px;margin:20px;">
<div data-fuse="23080803958"></div>
</div>
</div>
<p style="clear:both"></p>
</div>
<script src='js/tonegenerator.js'></script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','//www.google-analytics.com/analytics.js','ga');
if (window.location.host != 'localhost:4000') {
ga('create', 'UA-17960919-2', 'onlinetonegenerator.github.io');
ga('send', 'pageview');
window.onerror = function(message, file, line){
ga('send', 'event', 'JavaScript Error', message, file + ": Line "+ line, { 'nonInteraction': 1 });
}
}
</script>
</body>
</html>