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Homework Help: The speed of sound

  1. Apr 13, 2009 #1
    Please help!! trying to catch up with class! topic: the speed of sound

    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

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

    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. jcsd
  3. Apr 13, 2009 #2


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    Will it take some time to come back?
  4. Apr 13, 2009 #3
    i really have no idea. i missed two months of physics and now struggling.

    i think it took 870 ms to return.
  5. Apr 13, 2009 #4


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    ms means mili second and mili is 10^-3?
  6. Apr 13, 2009 #5


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    All units must be in same system (SI).

    length in meter
    time in second
  7. Apr 13, 2009 #6


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    is km/hour is SI unit of velocity?
  8. Apr 13, 2009 #7
    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

  9. Apr 13, 2009 #8


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    did you converted hour in sec?? it will be 5300*1000/3600 m/s
  10. Apr 13, 2009 #9
    i give up. i'm going to bed!

    good night! thanks for helping
  11. Apr 13, 2009 #10


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    d = v*t = (5300*1000/3600) m/s*(870/1000) s =
  12. Apr 14, 2009 #11
    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 [tex]\frac{1s}{1000ms}[/tex] = .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 [tex]\frac{1 min}{60s}[/tex] x [tex]\frac{1 hr}{60 min}[/tex] = 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:

    [tex]\frac{5300 km}{1 hr}[/tex] x [tex]\frac{1000 m}{1 km}[/tex] x [tex]\frac{1 hr}{60 min}[/tex] x [tex]\frac{1 min}{60 s}[/tex] = [tex]\frac{1472.222 m}{1 s}[/tex]

    [tex]\frac{1472.222 m}{1 s}[/tex] x .87s = 1280.83 m

    1280.83 / 2 = 640.4 m or .64 km
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