HP 20S: Acoustics Programs

HP 20S: Acoustics Programs

Program A: Speed of Sound in Dry Air

cs = 20.05 × √(273.15 + T°C)

Code:

01: 61, 41, A: LBL A

02: 75: +

03: 2: 2

04: 7: 7

05: 3: 3

06: 73: .

07: 1: 1

08: 5: 5

09: 74: =

10: 11: √

11: 55: ×

12: 2: 2

13: 0: 0

14: 73: .

15: 0: 0

16: 5: 5

17: 74: =

18: 61, 25: RTN

Program B: Mersenne's Law: Fundamental Frequency

f0 = √(F ÷ µ) ÷ (2 × L)

F: force (N)

µ: mass per unit length (kg/m)

L: string length (m)

f0: fundamental frequency (Hz)

(Marshall, pg. 19)

Store before running:

R1: force

R2: µ

R3: L

Code (continuing from the previous section):

19: 61, 41, b: LBL B

20: 33: (

21: 22, 1: RCL 1

22: 45: ÷

23: 22, 2: RCL 2

24: 34: )

25: 11: √

26: 45: ÷

27: 33: (

28: 2: 2

29: 55: ×

30: 22, 3: RCL 3

31: 34: )

32: 74: =

33: 61, 26: RTN

Program C: Standing Wavelength in an Open Pipe for the 1st through 5th Harmonic

λ = 2 × L ÷ n

L: length of the pipe

n: nth harmonic (positive integer)

(Marshall, pg. 21)

Code (continuing from the previous section):

34: 61, 41, C: LBL C

35: 21, 1: STO 1

36: 1: 1

37: 21, 2: STO 2

38: 61, 41, 3: LBL 3

39: 2: 2

40: 55: ×

41: 22, 1: RCL 1

42: 45: ÷

43: 22, 2: RCL 2

44: 74: =

45: 26: R/S

46: 1: 1

47: 21, 75, 2: STO+ 2

48: 22, 2: RCL 2

49: 31: INPUT

50: 5: 5

51: 61, 42: x≤y?

52: 51, 41, 3: GTO 3

53: 61, 26: RTN

Program D: Finding the perfect length and height for recording studios given the width.

Length = W × φ (stored in R1)

Width = W (stored in R2)

Height = W ÷ φ (stored in R3)

φ = (1 + √5) ÷ 2

(Marshall, pg. 34)

Code (continuing from the previous section):

54: 61, 41, d: LBL D

55: 21, 1: STO 1

56: 22, 2: STO 2

57: STO 3: STO 3

58: 33: (

59: 1: 1

60: 75: +

61: 5: 5

62: 11: √

63: 34: )

64: 45: ÷

65: 2: 2

66: 74: =

67: 21, 55, 1: STO× 1

68: 21, 45, 3: STO÷ 3

69: 22, 1: RCL 1

70: 26: R/S

71: 22, 2: RCL 2

72: 26: R/S

73: 22, 3: RCL 3

74: 61, 26: RTN

HP 20S - The Complete Code:

01: 61, 41, A: LBL A

02: 75: +

03: 2: 2

04: 7: 7

05: 3: 3

06: 73: .

07: 1: 1

08: 5: 5

09: 74: =

10: 11: √

11: 55: ×

12: 2: 2

13: 0: 0

14: 73: .

15: 0: 0

16: 5: 5

17: 74: =

18: 61, 25: RTN

19: 61, 41, b: LBL B

20: 33: (

21: 22, 1: RCL 1

22: 45: ÷

23: 22, 2: RCL 2

24: 34: )

25: 11: √

26: 45: ÷

27: 33: (

28: 2: 2

29: 55: ×

30: 22, 3: RCL 3

31: 34: )

32: 74: =

33: 61, 26: RTN

34: 61, 41, C: LBL C

35: 21, 1: STO 1

36: 1: 1

37: 21, 2: STO 2

38: 61, 41, 3: LBL 3

39: 2: 2

40: 55: ×

41: 22, 1: RCL 1

42: 45: ÷

43: 22, 2: RCL 2

44: 74: =

45: 26: R/S

46: 1: 1

47: 21, 75, 2: STO+ 2

48: 22, 2: RCL 2

49: 31: INPUT

50: 5: 5

51: 61, 42: x≤y?

52: 51, 41, 3: GTO 3

53: 61, 26: RTN

54: 61, 41, d: LBL D

55: 21, 1: STO 1

56: 22, 2: STO 2

57: STO 3: STO 3

58: 33: (

59: 1: 1

60: 75: +

61: 5: 5

62: 11: √

63: 34: )

64: 45: ÷

65: 2: 2

66: 74: =

67: 21, 55, 1: STO× 1

68: 21, 45, 3: STO÷ 3

69: 22, 1: RCL 1

70: 26: R/S

71: 22, 2: RCL 2

72: 26: R/S

73: 22, 3: RCL 3

74: 61, 26: RTN

Examples

LBL A:

Input: T = 0°C: Speed of sound: 331.371367011 m/s

Input: T = 10°C (50°F): Speed of sound: 337.82583835 m/s

Input: T = 26.66666667 (80°F) C: Speed of sound: 347.170058532 m/s

LBL B:

R1: 45 N, R2: 0.008 kg, R3: 0.06 m; f: 625 Hz

R1: 3 N, R2: 0.006 kg, R3: 0.058 m; f: 192.764480819 Hz

LBL C:

Open ended pipe length: 1.2 m

The wavelengths for the 1st, 2nd, 3rd, 4th, and 5th harmonics respectively:

2.4, 1.2, 0.8, 0.6, 0.48

Open ended pipe length: 0.059 m

The wavelengths for the 1st, 2nd, 3rd, 4th, and 5th harmonics respectively:

0.118, 0.059, 3.933333333E-2, 0.0295, 0.0236

LBL D:

Width: 12 ft; Length: 19.416407865 ft, Height: 7.416407865 ft

Width: 18 ft 6 in = 18.5 ft; Length: 29.9336287919 ft, 11.4336287919 ft

Source

Marshall, Steve. Acoustics: The Art of Sound. Wooden Books, LLC. San Rafael, California. 2023. ISBN 978-1-952178-33-7

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.

Casio fx-92 Collège: Plotting Lines, Regular Polygons, and Functions

Casio fx-92 Collège: Plotting Lines, Regular Polygons, and Functions

Introduction

The Casio fx-92 Collège has an algorithm application which is similar to Scratch. For more details, please refer to the Alogirthmique Mode section of my spotlight review:

https://edspi31415.blogspot.com/2025/02/spotlight-casio-fx-92-college.html

A limitation of the fx-92 Collège is that programs are not retained once we leave the Algorithmique Mode or turn the calculator off.

Remember that the commands, the mathematical functions, and keys on the calculator fx-92 Collège are in French. The left column is what will see on the calculator screen** (in French) and the right column is a “rough” translation to English. Please note that I am currently not fluent in French.

** Demander valuer is just shown as ? → var. (Prompt for a value)

** Metire var á is shown as expression → var. (Store an expression to a variable)

Draw a line y = Ax + B.

French: fx-92 Collegè	English Translation
(Demander valeur) ? → A	? → A
(Demander valeur) ? → B	? → B
(Metire var á) (-24 – B) ÷ A →C	(-24 – B) ÷ A →C
(Metire var á) (24 – B) ÷ A →D	(24 – B) ÷ A →D
Si C ≥ D Alors	If C ≥ D Then
(Metire var á) C →E	C →E
(Metire var á) D →C	D →C
(Metire var á) E →D	E →D
Fin	End
Stylo relevè	Pen is raised
Aller à x = C ; y = A×C + B	Go to C, A × C + B
S’ orienter à tan^-1(A) degrès	Set orientation to arctan(A) degrees
Stylo écrit	Pen is down
Avancer de √((D-C)^2 + 48^2) pixels	Move forward √((D-C)^2 + 48^2) pixels

The algorithm draws a line when -24 ≤ y ≤ 24. If x is in the range -96 ≤ x ≤ 95, the line will be plotted on the screen.

The algorithm solves the following equations:

A x + B = -24

A x + B = 24

where the minimum of the two results are stored in C and the maximum of the two results are stored in D.

The equation is given in standard form where A is the slope and B is the y-intercept. If we go to the left side of the line (Xmin) and head to the right, we can draw the line in the direction of the slope, which is calculated by arctan(A). The arc-tangent function typical has a range between -180° to 180° (-π radians to π radians).

Draw a Regular Polygon

Draw a regular polygon of B sides. The radius is fixed at 20 pixels. The polygon is drawn in the middle of the screen.

French: fx-92 Collegè	English Translation
(Demander valeur) ? → B	? → B
(Metire var á) 40 × sin(180° ÷ B) → C	40 × sin(180° ÷ B) → C
Stylo relevè	Pen raised
Aller à x = -C ÷ 2; y = -20	Go to -C ÷ 2, -20
(Metire var á) 1 → A	1 → A
Stylo écrit	Pen is down
Répéter jusqú a A>B	Repeat until A > B
Avancer de C pixels	Move forward C pixels
Tourner de ⟲ 360° ÷ B degrès	Turn (360° ÷ B) degrees
(Metire var á) 1 + A → A	1 + A → A
↑	End repeat loop

The program begins by determining the required side length and positioning the cursor to the point (-C/2, -20). This allows the polygon to drawn in the middle of the screen.

The relationship between the radius of regular polygon (r) and the side length (s) is:

s = 2 * r * sin(180° / n) = 2 * r * sin(π radians/n)

With r = 20, s = 40 * sin(180° / n)

The degree symbol is found in the Catalog → Angl/Coord/Sexag → Degrés.

The variable B is used for the number of sides.

Draw the Function C = f(z).

A = z minimum (Xmin), B = z maximum (Xmax)

Be aware that the plotting screen is limited and there is no ability to zoom. (-96 ≤ z ≤ 95)

The fx-92 errors if C < -999 or C > 999.

French: fx-92 Collegè	English Translation
(Demander valeur) ? → A	? → A
(Demander valeur) ? → B	? → B
(Metire var á) A→ z	A → z
Répéter jusqú a z >B	Repeat until z > B
(Metire var á) f(z)→ C (**)	f(z)→ C (**)
Si z = A Alors	If z = A Then (we are at the xmin at the graph)
Stylo relevè	Pen Raised
Sinon	Then
Stylo écrit	Pen is Down
Fin	End (If)
Aller à x = z ; y = C	Go to z ; C
(Metire var á) z + 0,5→ z	z + 0.5→ z
↑	End repeat loop

Here is where you enter you function. Examples may include:

15 × cos((z ÷ 10)^r ) (^r: Catalog → Angl/Coord/Sexag → Radians)

√z

Abs(z – 3) (Catalog → Cacul Numèrique → Value Absolue)

-2 × z + 1.1

e^(-z) (Catalog → Autre → select e)

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.

RPN: HP 32S & DM42: Converting Real Numbers to Hexadecimal Approximations

RPN: HP 32S & DM42: Converting Real Numbers to Hexadecimal Approximations

Introduction

We know calculators that have base conversions easily convert integers to different bases. But what about all real numbers? Not so much. Today’s blog will tackle it.

The procedure given today should work for converting from decimal to octal, binary, and hexadecimal. I chose hexadecimal:

0.A B C D… _16

The digit A is in units of 1/16.

The digit B is in units of 1/16^2 or 1/256.

The digit C is in units of 1/16^3 or 1/4096.

The digit D is in units of 1/16^2 or 1/65536.

and so on.

Note: The procedure considers positive real numbers only.

Example: Convert 7.86 to hexadecimal using 4 places

In hexadecimal, 4 places translates to terms of 1/65536.

Separate 7.86 into its integer and fractional parts.	Integer Part: 7 Fractional Part: 0.86
Convert the fractional part to n parts of 65536. (16^4)*	0.86 * 65536 = 56360.96
Round n to the nearest integer. Use the formula: int(n + 0.5) = int(n + 1/2)	Int(56360.96 + 0.5) = 53361 (round(56360.96, 0) = 53361)
Convert both original integer part and the last result to hexadecimal.	Integer Part: 7_10 → 7_16 Frac in terms of 65536: 53361_10 → DC29_16
**If the fractional part has less than four* digits showing in the calculator, pad the converted part with zeros on the left.
The approximate answer reads as:	7.86_10 → 7.DC29_16
Recall in Hexadecimal: A=10, B=11, C=12, D=13, E=14, F=15.

* precision: number of places.

HP 32S/HP 32SII/DM32 Code

H01 LBL H

H02 ENTER

H03 IP

H04 x<>y

H05 FP

H06 16

H07 4 (** - accuracy level, number of places)

H08 y^x

H09 ×

H10 2

H11 1/x

H12 +

H13 IP

H14 HEX

H15 STOP

H16 DEC

H17 RTN

HP 42S/DM42 Code

01 LBL “→HEX”

02 ENTER

03 IP

04 x<>y

05 FP

06 16

07 4 (** - accuracy level, number of places)

08 Y↑X

09 ×

10 0.5

11 +

12 IP

13 HEXM

14 STOP

15 EXITALL

16 RTN

When the program stops initially, the results are shown as follows:

Y: integer part

X: fractional part – right justified

Remember the number of places (precision) because if the fractional part has less digits, pad zeroes to the left.

Examples

n = precision = 4

Decimal	Y: Hex Integer	X: Hex Fractional (displayed)	Result (base 16)
3.5	3	8000	3.8000
π	3	243F	3.243F
√2	1	6A0A	1.6A0A
0.6732	0	AC57	0.AC57
0.0002	0	D	0.000D
e^4.1	3C	571D	3C.571D
8.2^1.7	23	C460	23.C460

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

All posts are 100% generated by human effort.  The author does not use AI engines and never will.