بسامد تواتر فرکانس

بَسامَد، تَواتُر یا فرکانس (به انگلیسی: frequency) به اندازه‌گیری تعداد دفعاتی گویند که یک رویداد تناوبی در واحد زمان اتفاق می‌افتد. برای محاسبه بسامد باید یک بازه زمانی را مشخص کرده، تعداد رخ دادن یک رویداد را در آن بازه زمانی شمرده و سپس این شماره را بر مدت آن بازه زمانی تقسیم کرد. راه دیگر محاسبه بسامد، اندازه‌گیری زمان میان دو رویداد پیاپی (تناوب) و سپس اندازه‌گیری بسامد به عنوان وارونه این زمان است: رابطه بسامد به این گونه‌است:


در این فرمول T همان تناوب است.

فرکانس اندازه گیری تعداد تکرار اتفاقی در واحد زمان است. برای محاسبه فرکانس بر روی یک بازه زمانی ثابت، تعداد دفعات وقوع یک حادثه را در آن بازه می شماریم و سپس این تعداد را بر طول بازه زمانی تقسیم می کنیم. پس از فیزیک دان آلمانی هاینریش رودولف هرتز، در سیستم واحدهای SI فرکانس با هرتز(Hz) اندازه گیری می‌شود. یک هرتز به این معنی است که یک واقعه یک بار بر ثانیه رخ می‌دهد.

واحدهای دیگری که برای اندازه گیری فرکانس بکار می‌روند به این شرح هستند: سیکل بر ثانیه، دور بر دقیقه (rpm). سرعت قلب توسط واحد ضربان بر دقیقه اندازه گیری می‌شود. یک روش جایگزین برای محاسبه فرکانس، اندازه گیری زمان بین دو رخداد متوالی حادثه‌ای است (دوره تناوب) و سپس محاسبه فرکانس به صورت عددی متقابل این زمان مانند زیر:


که در آن T دوره تناوب است.


فرکانس امواج در اندازه گیری فرکانس صدا، امواج الکترومغناطیسی (مانند امواج رادیویی یا نور )، سیگنال‌های الکتریکی یا دیگر امواج، فرکانس بر حسب هرتز، تعداد سیکل‌های شکل موج تکراری است. اگر موج یک صدا باشد، فرکانس آن چیزی است که زیر و بمی این موج را مشخص می‌کند.

فرکانس رابطه معکوسی با مفهوم طول موج دارد. فرکانس f برابر است با سرعت v یک موج تقسیم بر طول موج لاندااست که:


در موارد خاص که امواج الکترومغناطیسی از خلا عبور می‌کنند، v=c که در آن c برابر سرعت نور در خلا است و این عبارت به صورت زیر در می‌آید:


فرکانس‌های آماری [ویرایش]

در علم آمار فرکانس یک واقعه برابر است با تعداد دفعات رخ دادن یک حادثه در آزمایش یا مطالعه‌ای که صورت می‌گیرد. فرکانس‌ها معمولاً به صورت گرافیکی در نمودار هیستوگرام نمایش داده می‌شوند.

منابع [ویرایش]

ویکی‌پدیای انگلیسی

در ویکی‌انبار پرونده‌هایی دربارهٔ بسامد موجود است.
رده‌های صفحه: مفاهیم بنیادین فیزیک مکانیک امواج کمیت‌های فیزیکی صداشناسی لرزش و ارتعاشات مکانیکی کیفیت فکری فیلتر واکنش بسامدی
از ویکی پدیا
قس عربی
التردد أو التواتر هو مقیاس لتکرار حدث ما فی وحدة قیاس معیّنة. غالبًا ما یکون الحدیث عن وحدة قیاس زمنیة ما، وعندها تکون وحدة التردد هی الهرتس (Hz) والتی تعادل ، وتستخدم بشکل أساسی لقیاس مقدار تکرار الموجات. یکون تردد موجة دوریّة 1Hz إذا کانت تمر موجة کاملة فی نقطة ما، هی نقطة القیاس، خلال ثانیة واحدة. أی أنّه إذا قسنا فی لحظة معیّنة قیمة قصوى للموجة فی تلک النقطة، لن نحصل على نفس القیاس إلاّ بعد مرور ثانیة واحدة.
التردّد هو المفهوم المعاکس لمفهوم الدورة والتی تعرّف، حسب المثال السابق، کالفترة الزمنیة بین الحصول على قیاس أقصى فی الموجة فی نقطة معیّنة، إلى الحصول على نفس القیاس مرّة أخرى.
محتویات [أخف]
1 تعریف ووحدات
2 قیاس التردّد
3 تردّدات الأمواج
4 أمثلة
5 أنواع أخرى من التردّد
6 أنظر أیضًا
7 وصلات خارجیة
[عدل]تعریف ووحدات

یعرّف التردّد لأی عملیّة دوریّة تعود على نفسها کعدد المرّات التی تتکرّر فیها الدورة أو العملیّة خلال وحدة زمنیة معیّنة. یستخدم الحرف f أو لتمثیل التردّد فی العدید من المجالات الهندسیّة أو الفیزیائیّة کالبصریات والکهرباء وعلم الصوت والرادیو وغیرها.
الوحدة التقلیدیّة لقیاس التردّد هی الـHz أو الهرتس (والتی تعادل ) على اسم العالم الفیزیائی الألمانی هاینریخ هرتس. على سبیل المثال، فإذا کان تردّد عملیّة ما هو 1Hz، یعنی هذا أنّها تحصل مرّة کل ثانیة، أمّا إذا کان 2Hz، فإنّها تحصل مرّتین فی کل ثانیة، وهکذا. فإذا رمزنا لزمن الدورة بـ، تکون العلاقة بینه وبین التردد کالتالی:

بشرط أن یتم الحفاظ على وحدات الطرفین، فإذا کان التردد یقاس بوحدات الـHz، تکون وحدة زمن الدورة هی الثانیة.
فی بعض الاستعمالات هنالک وحدات خاصّة لقیاس التردّد. فمثلاً، لقیاس سرعة نبض القلب، تستعمل وحدة "نبضة فی الدقیقة" أو BPM) Beats per Minute)، ونفس الوحدة تستخدم فی عالم الموسیقى لقیاس الإیقاع. فی الحرکة الدائریّة تستخدم أحیانًا وحدة "دورة فی الدقیقة" أو rpm) Revolutions per Minute) لقیاس التردّد. لتحویل تلک الوحدات إلى الـHz تجب القسمة على .
[عدل]قیاس التردّد

لقیاس تردّد ظاهرة ما، یجب إحصاء عدد المرّات التی تتکرّر بها الظاهرة فی فترة زمنیة، ومن ثم القسمة على مدّة هذه الفترة.
فی الواقع، فمن المفضل على وجه العموم، ولغرض التدقیق، قیاس الفترة الزمنیة اللازمة لعدد محدّد مسبقًا من التکرارات، عوضًا عن قیاس عدد التکرارات الحاصلة خلال فترة زمنیّة محدّدة. هذا لأنّ التردّد قد لا یکون عددًا صحیحًا، کحرکة البندول المتأرجح. إنّ الطریقة الثانیة تؤدی إلى خطأ عشوائی فی القیاس یتراوح بین صفر إلى تکرّر واحد، أی إلى نصف تکرّر بالمعدّل، ممّا یؤدی إلى انحیاز فی تقدیرنا لـf. أمّا بالطریقة الأولى، فإنّنا نقیس وحدة زمنیة، والتی بالإمکان قیاسها بشکل أدق بواسطة ساعة.
[عدل]تردّدات الأمواج

بالإمکان تحلیل کل موجة إلى عدد من الأمواج التوافقیة (وفق تحلیل فورییه) الدّوریّة، ولکل موجة دوریّة هنالک علاقة بین تردّد الموجة لطول الموجة وسرعة تقدّمها:

بحیث أن:
هو تردّد الموجة
هی سرعتها و
هو طول الموجة
أی أن هنالک علاقة طردیة بین التردّد وسرعة الموجة، إذا حافظنا على طول الموجة، وعلاقة عکسیة بین تردّد وطول الموجة، إذا بقیت سرعتها ثابتة. فی الأمواج الکهرومغناطیسیّة، تستبدل القیمة عادًة بالقیمة للتنویه إلى سرعة الضوء.
عند انتقال أمواج کهرومغناطیسیّة تخرج عن مصدر أحادی اللون (أی مصدر یرسل أمواجًا کهرومغناطیسیّة ذات نفس طول الموجة) من وسط ذی معامل انکسار معیّن إلى وسط ذی معامل انکسار آخر، یتغیّر طول الأمواج وسرعتها، فی حین یبقى تردّدها ثابتًا، وهی ظاهرة تعرف بانکسار الضوء.
[عدل]أمثلة

بإمکان الأذن البشریّة أن تلتقط أمواجًا صوتیّة یتراوح تردّدها بین الـ20Hz والـ20 kHz. فی الواقع، فإنّ الأطفال یستطیعون سماع التردّدات حتّى الـ20 kHz، ولکن قدرة السمع فی مثل هذه الترددات المرتفعة تنخفض کلما کبر الإنسان بالسن.
إنّ تردّد التیار المتردّد فی المقابس الکهربائیّة البیتیّة فی أوروبا وأفریقیا وأسترالیا ومعظم آسیا هو 50Hz، ولکنّه بقیمة 60Hz فی معظم الأمریکیّتین.
تردّد الضوء المرئی من الطیف الکهرومغناطیسی یتراوح بین 430THz إلى 750THz.
[عدل]أنواع أخرى من التردّد

التردد الزاوی: یمثل بواسطة الحرف الیونانی ، ویصف سرعة التغیر فی طور موجة جسم یتذبذب حرکة توافقیة، مثلاً:

وحدة القیاس المتّبعة للتردد الزاوی هی رادیان فی الثانیة .
یجدر الذکر بأنّ هناک بعض التردّدات غیر الزمنیّة. فمثلاً، من الممکن الحدیث عن تردّد حیّزی فی صورة معیّنة، أو تردد لدالّة دوریّة معیّنة. فالتردّد الحیزی یمکن أن یکون، على سبیل المثال، عدد أزواج الخطوط السوداء والبیضاء فی المتر الواحد من صورة لخطوط سوداء وبیضاء. وفی هذه الحالة یستبدل متغیّر الزمن بأحد متغیّرات الفضاء.
[عدل]أنظر أیضًا

زمن دورة
مجال التردد
طول موجة
تردد طبیعی
[عدل]وصلات خارجیة

عنوان تعلیمی بالفیدیو :www.khanacademy.org
تصنیف: فیزیاء الأمواج
قس اردو
فریکوئنسی (انگریزی:Frequency) سے مراد تعدادارتعاشات ہوتی ہے جو کوئی مرتعش جسم ایک سکینڈ میں پوری کرے۔ جب کوئی لہر اٹھ کر دبتی ہے تو ہم کہتے ہیں کہ اس نے ایک چکر پورہ کرلیا۔ ایک لہر ایک سکنڈ میں ایسے جتنے چکر پورے کرتی ہے وہی اس کی فریکوئنسی ہوتی ہے۔
زمرہ جات:
صوتیات آواز
قس ترکی
Frekans veya titreşim sayısı bir olayın birim zaman (tipik olarak 1 saniye) içinde hangi sıklıkla, kaç defa tekrarlandığının ölçümüdür, matematiksel ifadeyle periyodun çarpmaya göre tersidir.
Konu başlıkları [gizle]
1 Ölçümü
2 Dalganın Frekansı
2.1 Frekanslar
3 Örnekler
[değiştir]Ölçümü

Bir olayın frekansını ölçmek için o olayın belirli bir zaman aralığında kendini kaç kere tekrar ettiği sayılır, sonra bu sayı zaman aralığına bölünerek frekans elde edilir.
SI birim sisteminde frekans, Hertz (Hz) ile gösterilir. Bir Hertz, bir olayın saniyede bir tekrarlandığı anlamına gelir. Olayın iki Hertzlik bir frekansa sahip olması ise, olayın saniyede kendini iki kere yinelediğini ifade eder. Frekansı ölçmenin başka bir yolu ise olayın kendini tekrar etmesi arasında geçen süreyi tayin etmektir zira frekans bu sürenin çarpmaya göre tersi olduğundan dolaylı olarak elde edilebilir. İki yineleme arasında geçen süreye periyot denir ve fizikte genellikle T ile gösterilir.

[değiştir]Dalganın Frekansı

Bir dalganın frekansı, dalgaboyuyla ilişkilidir. Dalganın dalgaboyuyla frekansının çarpımı, o dalganın hızını belirler. Dolayısıyla dalgaboyu bilinen bir dalganın frekansı bu ilişki kullanılarak belirlenebilir.

Bu ifadede v hızı λ (lambda) ise dalgaboyunu temsil eder. Özel bir durum olarak elektromanyetik bir dalga olan ışık boşlukta ışık hızıyla hareket ettiği için bu denklem

ifadesine dönüşür. Dalgalar bir ortamdan başka fiziksel yoğunluğa sahip bir ortama geçtiklerinde frekansları değişmez ancak hızları ve dolayısıyla dalgaboyları değişir. Doppler Etkisi dışında frekans hiçbir fiziksel olay dolayısıyla değişmez, diğer bir deyişle evrensel bir fiziksel değişmezdir.
[değiştir]Frekanslar
Sembol Aralık - Titreşim Sayısı Dalgaboyu
Extremely low frequency ELF 3 Hz ile 30 Hz 10,000 km ile 100,000 km
Super low frequency SLF 30 Hz ile 300 Hz 1,000 km ile 10,000 km
Ultra low frequency ULF 300 hz ile 3 Khz 100 km ile 1000 km
Very low frequency VLF 3 Khz ile 30 Khz 10 km ile 100 km
Low frequency LF 30 Khz ile 300 Khz 1 km ile 10 km
Medium frequency MF 300 Khz ile 3 Mhz 100 m ile 1 km
High frequency HF 3 Mhz ile 30 Mhz 10 m ile 100 m
Very high frequency VHF 30 Mhz ile 300 Mhz 1 m ile 10 m
Ultra high frequency UHF 300 Mhz ile 3 Ghz 10 cm ile 100 cm
Super high frequency SHF 3 Ghz ile 30 Ghz 1 cm ile 10 cm
Extremely high frequency EHF 30 Ghz ile 300 Ghz 1 mm ile 10 mm
[değiştir]Örnekler

Orkestrada bütünlüğü sağlamak için akort sesi olarak verilen la notası 440 Hz frekansına sahip bir titreşimdir.
İnsan kulağı 20-20.000 Hz aralığındaki titreşimlere tepki gösterir.
Şebekeden dağıtılan elektrik, saniyede 50 kere salınan alternatif gerilimdir. Elektrikli eşyaların üzerinde AC 220V 50Hz uyarısı cihazın, 50 Hz' lik 220 Volt genlikli alternatif akıma çalıştığı anlamına gelir.Detay için...
Kategoriler: Fiziksel niceliklerMekanik titreşimlerDalga mekaniğiAkustikTemel fizik kavramları
قس انگلیسی
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a newborn baby's heart beats at a frequency of 120 times a minute, its period (the interval between beats) is half a second.
Contents [hide]
1 Definitions and units
2 Measurement
2.1 By counting
2.2 By stroboscope
2.3 By frequency counter
2.4 Heterodyne methods
3 Frequency of waves
4 Examples
4.1 Physics of light
4.2 Physics of sound
4.3 Line current
5 Period versus frequency
6 Other types of frequency
7 Frequency ranges
8 See also
9 References
10 Further reading
11 External links
[edit]Definitions and units

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu).
In SI units, the unit of frequency is the hertz (Hz), named after the German physicist Heinrich Hertz: 1 Hz means that an event repeats once per second. A previous name for this unit was cycles per second.
A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated RPM. 60 RPM equals one hertz.[1]
The period, usually denoted by T, is the length of time taken by one cycle, and is the reciprocal of the frequency f:

The SI unit for period is the second.
[edit]Measurement



Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.
[edit]By counting
Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period, then dividing the count by the length of the time period. For example, if 71 events occur within 15 seconds the frequency is:

If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time.[2] The latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an average error in the calculated frequency of Δf = 1/(2 Tm), or a fractional error of Δf / f = 1/(2 f Tm) where Tm is the timing interval and f is the measured frequency. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small.
[edit]By stroboscope
An older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope. This is an intense repetitively flashing light (strobe light) whose frequency can be adjusted with a calibrated timing circuit. The strobe light is pointed at the rotating object and the frequency adjusted up and down. When the frequency of the strobe equals the frequency of the rotating or vibrating object, the object completes one cycle of oscillation and returns to its original position between the flashes of light, so when illuminated by the strobe the object appears stationary. Then the frequency can be read from the calibrated readout on the stroboscope. A downside of this method is that an object rotating at an integer multiple of the strobing frequency will also appear stationary.
[edit]By frequency counter
Higher frequencies are usually measured with a frequency counter. This is an electronic instrument which measures the frequency of an applied repetitive electronic signal and displays the result in hertz on a digital display. It uses digital logic to count the number of cycles during a time interval established by a precision quartz time base. Cyclic processes that are not electrical in nature, such as the rotation rate of a shaft, mechanical vibrations, or sound waves, can be converted to a repetitive electronic signal by transducers and the signal applied to a frequency counter. Frequency counters can currently cover the range up to about 100 GHz. This represents the limit of direct counting methods; frequencies above this must be measured by indirect methods.
[edit]Heterodyne methods
Above the range of frequency counters, frequencies of electromagnetic signals are often measured indirectly by means of heterodyning (frequency conversion). A reference signal of a known frequency near the unknown frequency is mixed with the unknown frequency in a nonlinear mixing device such as a diode. This creates a heterodyne or "beat" signal at the difference between the two frequencies. If the two signals are close together in frequency the heterodyne is low enough to be measured by a frequency counter. This process measures the difference between the unknown frequency and the reference frequency, which must be determined by some other method. To reach higher frequencies, several stages of heterodyning can be used. Current research is extending this method to infrared and light frequencies (optical heterodyne detection).
[edit]Frequency of waves

For periodic waves, frequency has an inverse relationship to the concept of wavelength; simply, frequency is inversely proportional to wavelength λ (lambda). The frequency f is equal to the phase velocity v of the wave divided by the wavelength λ of the wave:

In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes:

When waves from a monochrome source travel from one medium to another, their frequency remains exactly the same — only their wavelength and speed change.
[edit]Examples

[edit]Physics of light


Complete spectrum of electromagnetic radiation with the visible portion highlighted
Main articles: Light and Electromagnetic radiation
Visible light is an electromagnetic wave, consisting of oscillating electric and magnetic fields traveling through space. The frequency of the wave determines its color: 4×1014 Hz is red light, 8×1014 Hz is violet light, and between these (in the range 4-8×1014 Hz) are all the other colors of the rainbow. An electromagnetic wave can have a frequency less than 4×1014 Hz, but it will be invisible to the human eye; such waves are called infrared (IR) radiation. At even lower frequency, the wave is called a microwave, and at still lower frequencies it is called a radio wave. Likewise, an electromagnetic wave can have a frequency higher than 8×1014 Hz, but it will be invisible to the human eye; such waves are called ultraviolet (UV) radiation. Even higher-frequency waves are called X-rays, and higher still are gamma rays.
All of these waves, from the lowest-frequency radio waves to the highest-frequency gamma rays, are fundamentally the same, and they are all called electromagnetic radiation. They all travel through a vacuum at the speed of light.
Another property of an electromagnetic wave is its wavelength. The wavelength is inversely proportional to the frequency, so an electromagnetic wave with a higher frequency has a shorter wavelength, and vice-versa.
[edit]Physics of sound
Main article: Sound
Sound is made up of changes in air pressure in the form of waves. Frequency is the property of sound that most determines pitch.[3] The frequencies an ear can hear are limited to a specific range of frequencies.
Mechanical vibrations perceived as sound travel through all forms of matter: gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium. Sound cannot travel through a vacuum.
The audible frequency range for humans is typically given as being between about 20 Hz and 20,000 Hz (20 kHz). High frequencies often become more difficult to hear with age. Other species have different hearing ranges. For example, some dog breeds can perceive vibrations up to 60,000 Hz.[4]
[edit]Line current
In Europe, Africa, Australia, Southern South America, most of Asia, and Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the tone G), whereas in North America and Northern South America, the frequency of the alternating current in household electrical outlets is 60 Hz (between the tones B♭ and B; that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made, in countries using a European, or an American, grid frequency.
[edit]Period versus frequency

As a matter of convenience, longer and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are usually described by their frequency instead of period. These commonly used conversions are listed below:
Frequency 1 mHz (10−3) 1 Hz (100) 1 kHz (103) 1 MHz (106) 1 GHz (109) 1 THz (1012)
Period (time) 1 ks (103) 1 s (100) 1 ms (10−3) 1 µs (10−6) 1 ns (10−9) 1 ps (10−12)
[edit]Other types of frequency

Angular frequency ω is defined as the rate of change of angular displacement, θ, (during rotation), or the rate of change of the phase of a sinusoidal waveform (e.g. in oscillations and waves), or as the rate of change of the argument to the sine function:


Angular frequency is commonly measured in radians per second (rad/s) but, for discrete-time signals, can also be expressed as radians per sample time, which is a dimensionless quantity.
Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes. E.g.:


Wavenumber, k, sometimes means the spatial frequency analogue of angular temporal frequency. In case of more than one spatial dimension, wavenumber is a vector quantity.
[edit]Frequency ranges

The frequency range of a system is the range over which it is considered to provide a useful level of signal with acceptable distortion characteristics. A listing of the upper and lower limits of frequency limits for a system is not useful without a criterion for what the range represents.
Many systems are characterized by the range of frequencies to which they respond. Musical instruments produce different ranges of notes within the hearing range. The electromagnetic spectrum can be divided into many different ranges such as visible light, infrared or ultraviolet radiation, radio waves, X-rays and so on, and each of these ranges can in turn be divided into smaller ranges. A radio communications signal must occupy a range of frequencies carrying most of its energy, called its bandwidth. Allocation of radio frequency ranges to different uses is a major function of radio spectrum allocation.
[edit]See also

Electronics portal
Absolute threshold of hearing
Audible range
Bandwidth (signal processing)
Bandwidth extension
Bass (sound)
Coherence bandwidth
Critical band
Cumulative frequency analysis
Cutoff frequency
Downsampling
Electronic filter
Falsetto
Flashes Per Minute
Frequency converter
Frequency domain
Frequency distribution
Frequency extender
Frequency grid
Free spectral range
Frequency deviation
Frequency spectrum
Hearing range
High frequency limit
Hyperacusis
Interaction frequency
Musical acoustics
MVDDS dispute
Natural frequency
Negative frequency
Normalized frequency
Passband
Periodicity (disambiguation)
Piano key frequencies
Pink noise
Pitch (music)
Preselector
Power bandwidth
Range (music)
Radar signal characteristics
Radio window
Rate (mathematics)
Resonant frequency
Scientific pitch notation
Signaling (telecommunications)
Spectral width
Spread spectrum
Spectral component
Spectrum allocation
Symbol rate
Transition band
Transverter
Ultrasound
Upsampling
Wavelength
Whistle register
Wideband audio
[edit]References

^ Davies, A. (1997). New York: Springer. ISBN 9780412613203. http://books.google.com/?id=j2mN2aIs2YIC&pg=RA1-PA275.
^ Bakshi, K.A.; A.V. Bakshi, U.A. Bakshi (2008). Electronic Measurement Systems. US: Technical Publications. pp. 4–14. ISBN 9788184312065.
^ Pilhofer, Michael (2007). Music Theory for Dummies. For Dummies. p. 97.
^ Elert, Glenn; Timothy Condon (2003). "Frequency Range of Dog Hearing". The Physics Factbook. Retrieved 2008-10-22.
[edit]Further reading

Giancoli, D.C. (1988). Physics for Scientists and Engineers (2nd ed.). Prentice Hall. ISBN 013669201X
[edit]External links

Look up frequency or often in Wiktionary, the free dictionary.
National Research Council of Canada: Femtosecond comb; The measurement of optical frequencies
Conversion: frequency to wavelength and back
Conversion: period, cycle duration, periodic time to frequency
Keyboard frequencies = naming of notes - The English and American system versus the German system
Teaching resource for 14-16yrs on sound including frequency
A simple tutorial on how to build a frequency meter
Frequency - diracdelta.co.uk – JavaScript calculation.
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Categories: AcousticsFundamental physics conceptsMechanical vibrationsPhysical quantitiesQualities of thoughtWave mechanicsFilter frequency response