The document describes calculations to determine the depth of the Bristol Channel using its length, quarter wave resonance period, and the acceleration due to gravity. It shows rearranging the wave resonance equation to solve for depth and plugging in values for the Bristol Channel's length of 307km and quarter wave period of 12.5 hours. The calculation determines the depth is approximately 135 meters. It then repeats the calculation using only units, which cancels out variables and verifies the depth units are in meters.

1. 1 The Bristol Channel is 307km long and has a quarter
wave resonance period of 12.5 hours. How deep is it?
Acceleration due to gravity is 9.81ms-2. Repeat the
calculation using only units to show how they cancel out.

2. 1 • Rearrange the equation for h:

3. 1 • Rearrange the equation for h:
T =
16L2
gh

4. 1 • Rearrange the equation for h:
T =
16L2
gh
T2 =
16L2
gh

5. 1 • Rearrange the equation for h:
T =
16L2
gh
T2 =
16L2
gh
ghT2 = 16L2

6. 1 • Rearrange the equation for h:
T =
16L2
gh
T2 =
16L2
gh
ghT2 = 16L2
h =
16L2
gT2

7. 1 • Rearrange the equation for h:
T =
16L2
gh
T2 =
16L2
gh
ghT2 = 16L2
h =
16L2
gT2
• Substitute in the values you know, remembering to convert km to m and hours to seconds:

8. 1 • Rearrange the equation for h:
T =
16L2
gh
T2 =
16L2
gh
ghT2 = 16L2
h =
16L2
gT2
• Substitute in the values you know, remembering to convert km to m and hours to seconds:
h =
16 x (307,000)2
9.81 x (12.5 x 60 x 60)2 = ퟕퟓ. ퟗ퐦

9. 1 • Rearrange the equation for h:
T =
16L2
gh
T2 =
16L2
gh
ghT2 = 16L2
h =
16L2
gT2
• Substitute in the values you know, remembering to convert km to m and hours to seconds:
h =
16 x (307,000)2
9.81 x (12.5 x 60 x 60)2 = ퟕퟓ. ퟗ퐦
• Repeat the calculation using the units only:

10. 1 • Rearrange the equation for h:
T =
16L2
gh
T2 =
16L2
gh
ghT2 = 16L2
h =
16L2
gT2
• Substitute in the values you know, remembering to convert km to m and hours to seconds:
h =
16 x (307,000)2
9.81 x (12.5 x 60 x 60)2 = ퟕퟓ. ퟗ퐦
• Repeat the calculation using the units only:
m =
(m)2
ms−2. (s)2 =
m2
m
= 퐦