SMS-204: Integrative marine sciences.

Homework 6, Snell’s law and units conversion.

1.(50pts) Assume a three-layered fluid in which:

air Layer one: speed of sound 350m/s; Index of refraction 1.

Surface oceanLayer two (0-50m): Speed of sound 1470m/s; Index of refraction 1.337.

Subsurface ocean Layer three (depth>50m): Speed of sound 1430m/s; Index of refraction 1.34.

NOTE: Snell’s law: n1sin1=n2sin2.The ratio of the index of refraction is the inverse of the ratio of the propagation speed (n1/n2=v2/v1).

1.Compute how a ray of light coming down at 5 and 45degrees will refract as it is sent down from layer 1 (1=5, 45) towards layer 3? How will the ray refract if sent up from layer 3 as it interacts with the two interfaces (3=5, 45)?

2.Compute how a ray of sound coming down at 5 and 45degrees will refract as it is sent down from layer 1 (1=5, 45) towards layer 3? How will the ray refract if sent up from layer 3 as it interacts with the two interfaces (3=5, 45)?

Note: angles provided are measured between the direction of ray propagation and the vertical axis.

What are the implications in terms of transfer of sound and light between the atmosphere and oceans (Note that Excel uses radians rather then degrees when calculating trigonometric functions. To convert remember that radians=180degrees)?

2. Unit conversion (where appropriate convert all final results to MKS which stands for meters, kilograms, seconds. Please round results to two significant figures after the decimal when the answer is a fraction) (50/100):

Surface area of a 27cm3 cube.

Number of cm3 in 2 m3.

Volume of a 30-cm high and 15 cm in diameter cylinder.

Salt flux [M T-1] coming out of a salt marsh (density 1.02 g cm-3) in a channel that is 40 cm deep and 2 m wide where the velocity is 12 m s-1 and salt content is sufficient to make up 35 parts per thousand of the mass of the water+salt mixture.

Buoyancy force acting on a submerged wood log that is 8m long and 20 cm in diameter in fresh water (density of 1 g cm-3).

Speed of a vessel sailing at 6 kt (See, for example: ‘ for information about what a knot is.).

Surface are of the Earth in m2 (remember the circumference of the earth at the equator is approximately 24,900 mi).

Volume flux of a stream flowing at 4 mi h-1 that is 10 yd wide and 1 ft deep.

Minimum number of 50-ml syringes needed to inject a 5 × 10-5 m3 dose of a drug to a whale.

Heart rate of 75 pulses min-1.

Boss, 2018

This page was last edited on 9/27/2018