A disc record exhibits a variable frequency response. Since its tangential velocity varies, it has the largest range of response at the outer edge of the recording and it decreases towards the center.

The size of a phono stylus must be small enough so as to contain no more than one half of a cycle of a signal within the width as it passes by. In other words, the stylus dimension must be at least one half the wavelength of the signal of interest. Using general intuition, you can imagine that if the stylus only needed to be the width of one cycle of the highest frequency signal of interest, then the positive and negative portions of that signal would cancel out as it passed through that portion of the groove. Elliptical styli produce higher frequency response compared to their conical counterparts because a smaller dimension is occupied tangential to the groove with that smaller dimension in actual contact with the groove wall.

The following equations pertain:

W = V / F x 2

wherein -

W = Smallest dimension of the styli (in inches)

V = Tangential Velocity of the record at the point of interest (in inches per second)

F = Maximum reproducible frequency (in Hz or cycles per second)

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Considering a constant angular velocity rotating disc (like a Vinyl LP record), the following formula describes its tangential velocity:

V = Pi x D x RPM / 60

wherein

D = Usable Diameter of the Record at various locations (in inches)

RPM = Constant Angular Velocity of the Record in Revolutions per Minute

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combining & simplifying the above equations and solving for Frequency (F in Hz)

wherein

D = Usable Diameter of the Record at various locations (in inches)

RPM = Revolutions Per Minute of the Record in Question

W = Smallest dimension of the styli (in inches)

Pi

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Now, lets calculate the maximum theoretical frequency response of some common records played with some common styli types using the above equation for each:

This type of record has 11.5 inches on its outer most edge and 6 inches on its inner most edge (by inspection).

Using an elliptical 0.7 x

Theoretical Starting Frequency Response:

Theoretical Ending Frequency Response:

Response Variance:

Average Response:

This type of record has 6.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 0.7 x

Theoretical Starting Frequency Response:

Theoretical Ending Frequency Response:

Response Variance:

Average Response:

This type of record has 9.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x

Theoretical Starting Frequency Response:

Theoretical Ending Frequency Response:

Response Variance:

Average Response:

This type of record has 11.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x

Theoretical Starting Frequency Response:

Theoretical Ending Frequency Response:

Response Variance:

Average Response:

This type of record has 15.5 inches on its outer most edge and 8.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x

Theoretical Starting Frequency Response:

Theoretical Ending Frequency Response:

Response Variance:

Average Response:

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Note: Interestingly, the 45 RPM Record seems to be the most optimal design if the requirement for audio reproduction is limited to 20 KHz.

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The size of a phono stylus must be small enough so as to contain no more than one half of a cycle of a signal within the width as it passes by. In other words, the stylus dimension must be at least one half the wavelength of the signal of interest. Using general intuition, you can imagine that if the stylus only needed to be the width of one cycle of the highest frequency signal of interest, then the positive and negative portions of that signal would cancel out as it passed through that portion of the groove. Elliptical styli produce higher frequency response compared to their conical counterparts because a smaller dimension is occupied tangential to the groove with that smaller dimension in actual contact with the groove wall.

The following equations pertain:

W = V / F x 2

wherein -

W = Smallest dimension of the styli (in inches)

V = Tangential Velocity of the record at the point of interest (in inches per second)

F = Maximum reproducible frequency (in Hz or cycles per second)

-----------------------------------------

Considering a constant angular velocity rotating disc (like a Vinyl LP record), the following formula describes its tangential velocity:

V = Pi x D x RPM / 60

wherein

D = Usable Diameter of the Record at various locations (in inches)

RPM = Constant Angular Velocity of the Record in Revolutions per Minute

-----------------------------------------

combining & simplifying the above equations and solving for Frequency (F in Hz)

**F = (Pi x D x RPM) / (W x 120)**wherein

D = Usable Diameter of the Record at various locations (in inches)

RPM = Revolutions Per Minute of the Record in Question

W = Smallest dimension of the styli (in inches)

Pi

__~__3.1416-----------------------------------------

Now, lets calculate the maximum theoretical frequency response of some common records played with some common styli types using the above equation for each:

**1. 33 1/3rd RPM, 12 Inch Record**This type of record has 11.5 inches on its outer most edge and 6 inches on its inner most edge (by inspection).

Using an elliptical 0.7 x

__0.3__mil phono stylus, the frequency response will be as follows:Theoretical Starting Frequency Response:

**33.33 KHz**Theoretical Ending Frequency Response:

**17.5 KHz**Response Variance:

**15.83 KHz**Average Response:

**25.42 KHz****2. 45 RPM, 7 Inch Record**This type of record has 6.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 0.7 x

__0.3__mil phono stylus, the frequency response will be as follows:Theoretical Starting Frequency Response:

**25.5 KHz**Theoretical Ending Frequency Response:

**17.6 KHz**Response Variance:

**7.9 KHz**Average Response:

**21.55 KHz****3. 78 RPM, 10 Inch Record**This type of record has 9.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x

__1.2__mil phono stylus, the frequency response will be as follows:Theoretical Starting Frequency Response:

**16.25 KHz**Theoretical Ending Frequency Response:

**7.7 KHz**Response Variance:

**8.55 KHz**Average Response:

**11.97 KHz****4. 78 RPM, 12 Inch Record**This type of record has 11.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x

__1.2__mil phono stylus, the frequency response will be as follows:Theoretical Starting Frequency Response:

**19.57 KHz**Theoretical Ending Frequency Response:

**7.7 KHz**Response Variance:

**11.87 KHz**Average Response:

**13.64 KHz****5. 33 RPM, 16 Inch Acetate Transcription Record**This type of record has 15.5 inches on its outer most edge and 8.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x

__1.2__mil phono stylus, the frequency response will be as follows:Theoretical Starting Frequency Response:

**11.27 KHz**Theoretical Ending Frequency Response:

**6.18 KHz**Response Variance:

**5.09 KHz**Average Response:

**8.73 KHz**-----------------------------------------

Note: Interestingly, the 45 RPM Record seems to be the most optimal design if the requirement for audio reproduction is limited to 20 KHz.

keyword: record frequency response, frequency response of record, stylus effect on response, speed effect on response, frequency resolving, stylus frequency response, record frequency response, frequency response of records, disc frequency response, record frequency range, response of records, recording frequency response, freq response of records, record freq response, 78 record frequency response, 45 rpm record frequency response, transcription record frequency response, transcription frequency response

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