Resonance & Peak Displacements

Formulas

D R = 77.5 * 2.8 * Pf/Po

*(Q/Fr *Nr^0.5)

Peak to Peak

Pf = 165dB

Pf/Pa = 1/1400

D R = 77.5 * Pf/Po

*(Q/Fr *Nr^0.5)

RMS

Q=10

K= 77.5

PTP = RMS X 2.8

Column Legends

F @ r

D R (microns) PTP

D R (microns) RMS

D R (microns) PTP

D R (microns) RMS

N

Nr

Depth Ft.

Peak to Peak

RMS

Using Nr

Using Nr

Using N

Using N

SPECIAL CASES

"Mid-Range" Sonar

165dB

165dB

165dB

165dB

Mu1= 1x10^6

F @ r

D R PTP Nr

D R RMS Nr

D R PTP N

D R RMS N

N

Nr

Depth Ft.

Test Case (Tepley Fig. 2)

3500

3.55

1.27

3.63

1.30

9.3104

9.73

265.77

Cuvier Pterygoid Sinus

3500

0.92

0.33

0.92

0.33

144.9825

143.50

4604.56

Cuvier Lung 3500Hz **

3500

0.13

0.05

0.13

0.05

1115.680

1,100.53

35647.47

Mu1 = 1x10^7

Test Case (Tepley Fig. 2)

3500

3.55

1.27

4.79

1.71

5.34105

9.73

138.83

Cuvier Pterygoid Sinus

3500

0.92

0.33

0.94

0.33

139.914

143.50

4442.47

Cuvier Lung 3500Hz **

3500

0.13

0.05

0.13

0.05

1110.546

1,100.53

35483.28

Breath Holding

e.g. Chris Reid Case

for Mu1 = 1x10^7

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Human Lung Female 0ft

101

76.06

27.16

153.01

54.65

1.00000

4.05

0.00

Human Lung Female 10ft

113

64.26

22.95

120.19

42.92

1.31280

4.59

10.00

Human Lung Female 20ft

123

56.05

20.02

99.17

35.42

1.62540

5.09

20.00

for Mu1= 1x10^6

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Human Lung Female 0ft

44

292.71

104.54

355.24

126.87

1.00000

1.47

0.00

Human Lung Female 10ft

51

224.78

80.28

262.88

93.89

1.31280

1.80

10.00

Human Lung Female 20ft

59

180.87

64.60

206.24

73.66

1.62540

2.11

20.00

SCUBA

e.g. Jay Muller Case

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Mu1 = 1x10^7

SCUBA Male 30 Hz

30

499.36

178.34

2,563.92

915.68

0.04000

1.05

-30.70

Mu1= 1x10^6

SCUBA Male 30 Hz

30

505.36

180.49

667.63

238.44

0.59880

1.05

-12.83

SCUBA Divers

Male

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Mu1 = 1x10^7

SCUBA Male 0 ft

93

82.94

29.62

166.98

59.64

1.00000

4.05

0.00

SCUBA Male 10 ft

94

80.98

28.92

143.57

51.28

1.31280

4.13

10.00

SCUBA Male 20 ft

96

79.12

28.26

127.17

45.42

1.62540

4.20

20.00

SCUBA Male 50 ft

100

74.07

26.45

97.17

34.70

2.56350

4.41

50.00

SCUBA Male 100 ft

106

67.08

23.96

71.98

25.71

4.12699

4.75

100.00

SCUBA Male 200 ft

118

56.73

20.26

48.90

17.46

7.25400

5.39

200.00

SCUBA Male 300 ft

128

49.40

17.64

37.49

13.39

10.38100

5.98

300.00

Mu1= 1x10^6

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

SCUBA Male 0 ft

40

316.58

113.06

385.68

137.74

1.00000

1.48

0.00

SCUBA Male 10 ft

43

280.72

100.26

312.24

111.52

1.31280

1.62

10.00

SCUBA Male 20 ft

46

252.88

90.32

262.89

93.89

1.62540

1.76

20.00

SCUBA Male 50 ft

54

196.90

70.32

179.02

63.94

2.56350

2.12

50.00

SCUBA Male 100 ft

65

146.46

52.31

117.27

41.88

4.12699

2.65

100.00

SCUBA Male 200 ft

83

99.64

35.59

69.53

24.83

7.25400

3.53

200.00

SCUBA Male 300 ft

97

76.91

27.47

49.44

17.66

10.38100

4.29

300.00

Female

Mu1 = 1x10^7

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

SCUBA Female 0 ft

101

75.91

27.11

152.83

54.58

1.00000

4.05

0.00

SCUBA Female 10 ft

103

74.12

26.47

131.40

46.93

1.31280

4.13

10.00

SCUBA Female 20 ft

104

72.41

25.86

116.39

41.57

1.62540

4.20

20.00

SCUBA Female 50 ft

109

67.79

24.21

88.94

31.76

2.56350

4.41

50.00

SCUBA Female 100 ft

116

61.40

21.93

65.88

23.53

4.12699

4.75

100.00

SCUBA Female 200 ft

129

51.92

18.54

44.75

15.98

7.25400

5.39

200.00

SCUBA Female 300 ft

140

45.21

16.15

34.31

12.25

10.38100

5.98

300.00

Mu1= 1x10^6

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

SCUBA Female 0 ft

44

289.74

103.48

352.99

126.07

1.00000

1.48

0.00

SCUBA Female 10 ft

47

256.92

91.76

285.78

102.06

1.31280

1.62

10.00

SCUBA Female 20 ft

51

231.45

82.66

240.61

85.93

1.62540

1.76

20.00

SCUBA Female 50 ft

59

180.21

64.36

163.85

58.52

2.56350

2.12

50.00

SCUBA Female 100 ft

71

134.05

47.87

107.33

38.33

4.12699

2.65

100.00

SCUBA Female 200 ft

90

91.19

32.57

63.63

22.73

7.25400

3.53

200.00

SCUBA Female 300 ft

106

70.39

25.14

45.25

16.16

10.38100

4.29

300.00

HUMAN LUNG

Adult Male Lung

6 L. @ surface

Mu1 = 1x10^6

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Human Lung (frm Birch) @ 5 M

52

212.78

75.99

244.60

87.36

1.51300

2.00

16.41

Human Lung Male 0 ft

40

319.81

114.22

388.14

138.62

1.00000

1.47

0.00

Human Lung Male 10 ft

47

245.60

87.71

287.22

102.58

1.31280

1.80

10.00

Human Lung Male 20 ft

54

197.62

70.58

225.34

80.48

1.62540

2.11

20.00

Human Lung Male 100Hz

101

72.51

25.90

76.76

27.41

4.00000

4.48

95.94

Human Lung Male 200Hz

201

24.18

8.64

24.69

8.82

9.80000

10.21

281.42

Human Lung Male 300Hz

301

12.63

4.51

12.76

4.56

16.30000

16.63

489.29

Human Lung Male 500Hz

501

5.59

2.00

5.60

2.00

30.50000

30.63

943.41

Human Lung Male 1000Hz

1000

1.85

0.66

1.84

0.66

70.70000

70.27

2229.01

Mu 1 = 1 x 10^7

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Human Lung (frm Birch) @ 5 M

109

64.14

22.91

115.61

41.29

1.51300

4.91

16.41

Human Lung Male 0 ft

93

83.10

29.68

167.18

59.71

1.00000

4.05

0.00

Human Lung Male 10 ft

103

70.21

25.07

131.32

46.90

1.31280

4.59

10.00

Human Lung Male 20ft

112

61.24

21.87

108.35

38.70

1.62540

5.09

20.00

Human Lung Male 100Hz

100

73.51

26.25

140.19

50.07

1.22000

4.44

7.04

Human Lung Male 200Hz

200

24.23

8.65

32.25

11.52

5.76000

10.20

152.22

Human Lung Male 300Hz

300

12.66

4.52

15.02

5.36

11.80000

16.59

345.38

Human Lung Male 500Hz

501

5.60

2.00

6.11

2.18

25.70000

30.61

789.91

Human Lung Male 1000Hz

1000

1.85

0.66

1.91

0.68

65.70000

70.26

2069.11

Human Lung Female

4.6 Liters @surface

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Human Lung Female 0 ft

44

292.71

104.54

355.24

126.87

1.00000

1.47

0.00

Human Lung Female 10 ft

51

224.78

80.28

262.88

93.89

1.31280

1.80

10.00

Human Lung Female @ 20ft

59

180.87

64.60

206.24

73.66

1.62540

2.11

20.00

Human Lung Female 100Hz

100

77.60

27.71

82.82

29.58

3.50000

3.99

79.95

Human Lung Female 200Hz

200

25.53

9.12

26.14

9.34

8.75000

9.18

247.85

Human Lung Female 300Hz

300

13.38

4.78

13.54

4.83

14.55000

14.90

433.33

Human Lung Female 500Hz

501

5.90

2.11

5.92

2.11

27.35000

27.52

842.67

Human Lung Female 1000Hz

1000

1.95

0.70

1.94

0.69

63.50000

63.17

1998.75

Mu 1 = 1 x 10^7

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Human Lung Female 0 ft

101

76.06

27.16

153.01

54.65

1.00000

4.05

0.00

Human Lung Female 10 ft

113

64.26

22.95

120.19

42.92

1.31280

4.59

10.00

Human Lung Female 20ft

123

55.95

19.98

98.92

35.33

1.63000

5.10

20.15

Human Lung Female 100Hz

101

77.00

27.50

155.76

55.63

0.98000

4.01

-0.64

Human Lung Female 200Hz

200

25.53

9.12

35.12

12.54

4.85000

9.18

123.12

Human Lung Female 300Hz

300

13.38

4.78

16.21

5.79

10.16000

14.90

292.94

Human Lung Female 500Hz

500

5.91

2.11

6.52

2.33

22.60000

27.52

690.77

Human Lung Female 1000Hz

1000

1.95

0.70

2.02

0.72

58.55000

63.19

1840.45

Pterygoid Sinus Cuvier

835cc at surface

Mu 1 = 1 x 10^6

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Pterygoid Sinus 100Hz

101

107.56

38.42

123.31

44.04

1.55000

2.04

17.59

Pterygoid Sinus 200Hz

200

35.98

12.85

38.01

13.57

4.15000

4.63

100.74

Pterygoid Sinus 300Hz

301

18.76

6.70

19.34

6.91

7.10000

7.55

195.08

Pterygoid Sinus 500Hz

501

8.30

2.96

8.41

3.00

13.55000

13.91

401.35

Pterygoid Sinus 1000Hz

1000

2.74

0.98

2.75

0.98

31.82000

31.93

985.62

Mu 1 = 1 x 10^7

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Pterygoid Sinus 100Hz

101

108.24

38.66

344.62

123.08

0.20000

2.03

-25.58

Pterygoid Sinus 200Hz

200

35.92

12.83

66.81

23.86

1.34000

4.64

10.87

Pterygoid Sinus 300Hz

300

18.82

6.72

27.80

9.93

3.45000

7.53

78.35

Pterygoid Sinus 500Hz

500

8.32

2.97

10.22

3.65

9.20000

13.89

262.24

Pterygoid Sinus 1000Hz

1000

2.74

0.98

2.98

1.06

27.02000

31.93

832.12

Cuvier Lung

136 liter at surface

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Cuvier Lung 100Hz

100

39.44

14.09

39.89

14.24

15.10000

15.44

450.92

Cuvier Lung 200Hz

200

12.97

4.63

12.98

4.64

35.50000

35.56

1103.31

Cuvier Lung 300Hz

300

6.80

2.43

6.78

2.42

58.00000

57.74

1822.86

Cuvier Lung 500Hz

500

3.00

1.07

2.99

1.07

107.50000

106.55

3405.87

Cuvier Lung 1000Hz

1000

0.99

0.35

0.98

0.35

247.80000

244.87

7892.66

Mu 1 = 1 x 10^7

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Cuvier Lung 100Hz

100

39.40

14.07

47.35

16.91

10.70000

15.46

310.21

Cuvier Lung 200Hz

200

13.00

4.64

14.00

5.00

30.60000

35.50

946.61

Cuvier Lung 300Hz

301

6.77

2.42

7.06

2.52

53.20000

57.90

1669.36

Cuvier Lung 500Hz

500

3.00

1.07

3.06

1.09

102.50000

106.59

3245.97

Cuvier Lung 1000Hz

1000

0.99

0.35

0.99

0.36

242.70000

244.87

7729.57

Dolphin Lung

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Dolphin Lung 100Hz

101

82.54

29.48

89.02

31.79

3.00000

3.49

63.96

Dolphin Lung 200Hz

201

27.34

9.76

28.13

10.05

7.55000

7.99

209.47

Dolphin Lung 300Hz

300

14.33

5.12

14.54

5.19

12.60000

12.98

370.97

Dolphin Lung 500Hz

484

6.68

2.39

6.72

2.40

22.75000

22.99

695.57

Dolphin Lung 1000Hz

1000

2.09

0.75

2.09

0.74

55.20000

54.98

1733.32

Mu 1 = 1 x 10^7

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Dolphin Lung 100Hz

101

82.47

29.45

181.62

64.87

0.72000

3.49

-8.95

Dolphin Lung 200Hz

201

27.30

9.75

39.41

14.07

3.84000

8.00

90.82

Dolphin Lung 300Hz

301

14.30

5.11

17.84

6.37

8.35000

13.00

235.05

Dolphin Lung 500Hz

501

6.33

2.26

7.09

2.53

19.05000

23.95

577.24

Dolphin Lung 1000Hz

1000

2.09

0.75

2.19

0.78

50.24000

54.97

1574.70

Finback Lung

2000 Liters

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Finback Lung 100Hz

101

22.81

8.15

22.96

8.20

45.00000

45.60

1485.00

Finback Lung 200Hz

200

7.59

2.71

7.61

2.72

103.50000

104.14

3415.50

Finback Lung 300Hz

301

3.96

1.41

3.96

1.42

169.00000

169.68

5577.00

Finback Lung 500Hz

501

1.75

0.63

1.75

0.63

312.00000

312.77

10296.00

Finback Lung 1000Hz

1001

0.58

0.21

0.58

0.21

717.00000

718.02

23661.00

Mu 1 = 1 x 10^7

F @ r

D R N ptp

D R N rms

D R Nr ptp

D R Nr rms

N

Nr

Depth Ft.

Finback Lung 100Hz

100

22.88

8.17

24.40

8.71

40.00000

45.50

1320.00

Finback Lung 200Hz

200

7.58

2.71

7.80

2.78

98.50000

104.17

3250.50

Finback Lung 300Hz

301

3.95

1.41

4.02

1.44

164.00000

169.76

5412.00

Finback Lung 500Hz

501

1.75

0.62

1.77

0.63

307.00000

312.88

10131.00

Finback Lung 1000Hz

1001

0.58

0.21

0.58

0.21

712.00000

718.15

23496.00