# The speed of sound

1. Apr 13, 2009

### dlre

1. The problem statement, all variables and given/known data

Determine the depth of water if an echo using sonar returns in 870 ms and the speed of sound in water is 5300 km/h.

2. Relevant equations

distance= speed * time
depth=distance/2

3. The attempt at a solution
time= 870s
speed= 5300km/h

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i'm stuck at the part on converting ms to h. i think the

the answer i got is 0.64km

870ms= 0.00024167h
distance = 5300*0.00024167 = 1.28
depth= 1.28/2 = 0.64

Last edited: Apr 13, 2009
2. Apr 13, 2009

### mukundpa

Will it take some time to come back?

3. Apr 13, 2009

### dlre

i really have no idea. i missed two months of physics and now struggling.

i think it took 870 ms to return.

4. Apr 13, 2009

### mukundpa

ms means mili second and mili is 10^-3?

5. Apr 13, 2009

### mukundpa

All units must be in same system (SI).

length in meter
time in second

6. Apr 13, 2009

### mukundpa

is km/hour is SI unit of velocity?

7. Apr 13, 2009

### dlre

isn't it?

does it matter?

if we'redoing this by meter and second, then this is my attempt

d= 5300000m/s *0.87 s = 4,611,000m
depth= 4,611,000/2 = 2,305,500

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8. Apr 13, 2009

### mukundpa

did you converted hour in sec?? it will be 5300*1000/3600 m/s

9. Apr 13, 2009

### dlre

i give up. i'm going to bed!

good night! thanks for helping

10. Apr 13, 2009

### mukundpa

d = v*t = (5300*1000/3600) m/s*(870/1000) s =

11. Apr 14, 2009

### 3.211k

Your answer of .64km looks good to me (and seems like a reasonable depth). So this question seems to be mainly about unit conversions.
Start with 870 ms . Now we know that ms means milliseconds, and that milli means 10^-3
So 870 ms = 870 x 10^-3 s = .87 s

Or another way to think about this is to multiply the 870ms with the correct ratios to cancel out the ms units so that you are left with seconds :

870 ms x $$\frac{1s}{1000ms}$$ = .87s
Here you are left with seconds; as you can see the milliseconds have canceled out.

You could continue to convert this into hours:

.87s x $$\frac{1 min}{60s}$$ x $$\frac{1 hr}{60 min}$$ = 2.416...x 10^-4 hr
Here we are left with hours since the units of seconds and minutes have been eliminated.

Now for the question:

$$\frac{5300 km}{1 hr}$$ x $$\frac{1000 m}{1 km}$$ x $$\frac{1 hr}{60 min}$$ x $$\frac{1 min}{60 s}$$ = $$\frac{1472.222 m}{1 s}$$

$$\frac{1472.222 m}{1 s}$$ x .87s = 1280.83 m

1280.83 / 2 = 640.4 m or .64 km