# I need help on my homework

1. Sep 2, 2006

### vincikai

i need help on my homework!!

One way to monitor global warming is to measure the average temperature of the ocean. Researchers are doing this by measuring the time it takes sound pulses to travel underwater over large distances. At a depth of 1000 m, where ocean temperatures hold steady near 4C, the average sound speed is . It's known from laboratory measurements that the sound speed increases for every 1.0C increase in temperature. In one experiment, where sounds generated near California are detected in the South Pacific, the sound waves travel 7600 .

If the smallest time change that can be reliably detected is 1.0 s, what is the smallest change in average temperature that can be measured?

2. Sep 2, 2006

### vincikai

have anyone else also use masteringphysics for their homework!!? i hate how they grade physics homework through a poorly design and fuked@#%%^%up program.

3. Sep 2, 2006

### HallsofIvy

Staff Emeritus
I you sure you read the instructions carefully? You didn't read the instructions on where to put homework very carefully!

4. Sep 4, 2006

### andrevdh

This looks like a candidate for error analysis. See for example:

especially the general formula given in (f) Other Functions: Getting formulas using partial derivatives

Personally I would approach it from the speed of sound side. Taking that the speed of sound is a function of the temperature, T, distance travelled, d, and time, t, to travel this distance. That is

$$v = f(T,d,t)$$

It seems the formula for your problem is of the form

$$v = v_o +\alpha (T - 4)$$

where $$\alpha$$ is the increase in the speed of sound per unit temperature increase above four degrees.

5. Jan 18, 2007

### kirbykirbykirby

Bump. I don't understand where this formula comes from. The answer in the textbook is 0.07 degrees celsius. Can I have some more hints please? Sorry, I don't understand. :uhh:

6. Jan 20, 2008

### bitethebullet

Solution Hints

What andrevdh said is somewhat irrelevant as it doesn't deal with what's being asked or with the information given.

You know how far the sound has traveled and you know the ideal speed.
Manipulating velocity=distance/time, you get time=distance/velocity.

You want to find the effect of a 1 second decrease in the time it takes for the sound to travel on the velocity of that sound and consequently the temperature.

Try subtracting a second from your time that you got above and translating that into velocity using your distances. From there, you should be able to deduce, perhaps using proportions or something, how large of a change you get in temperature from a change in time.

Hope this helps.