Question

Measuring the speed of sound in the ocean is an important part of marine research. One application is the study of climate change. The speed of sound depends on the temperature, salinity, and depth below the surface. For a fixed temperature of 25 degrees Celsius and salinity of 35 parts per thousand, the speed of sound is a function of the depth. At the surface, the speed of sound is 1534 meters per second. For each increase in depth by 1 kilometer, the speed of sound increases by 17 meters per second. Use D for depth (in kilometers) and S for the speed of sound (in meters per second), and find a linear formula for S as a function of D.

Answer 1

A linear formula for S as a function of D is S=17D+1534

Explanation:

We are supposed to find a linear formula for S as a function of D.

Equation of line : y = mx+c

We are given that At the surface, the speed of sound is 1534 meters per second.

c = 1534

We are given that for each increase in depth by 1 km, the speed increases by 17 m/s

So, Slope = m = 17

Substitute the values in equation

y=17x+1534

x denotes depth

y denotes speed

We are given that Use D for depth and S for the speed of sound

So, S=17D+1534

Hence a linear formula for S as a function of D is S=17D+1534