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
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