# Calculating the speed of sound in water

Harini Krishna
Hi,

i want to calculate the speed of sound in water
Containing
Chlorine : 4mg/L in 1L distill Water

Chloroamine : 4mg/L in 1L distill Water

Florides : 0.5mg/L + in 1L distill Water

Copper : 0.005mg/L + in 1L distill Water

Lead : 1.3 mg/L in 1L distill Water

Thankyou
Warm Regards
Harini Krishna

Homework Helper
Gold Member
Are you wanting to do an experiment to calculate it? Or are you wanting to calculate it based on the density of the liquid?

In the first case, there are several experiments demonstrated online, using a tube and a sound generator.

If it is the second case, does your textbook discuss how the density of the medium affects the speed of sound?

Gold Member
The formula for these situations can be found at Engineering Toolbox.

Speed of Sound

I would effectively consider it to be identical to the speed of sound in pure water, given how small the levels of those contaminants are.

Gold Member
I would effectively consider it to be identical to the speed of sound in pure water, given how small the levels of those contaminants are.
It adds up to a little less than 10mg of impurities dissolved in each 1,000,000mg of water.
Even if all of that were lead, it would still mass the same as water to within one part in 10,000.

But hey, that won't change the math.

i want to calculate the speed of sound in water
Containing
Chlorine : 4mg/L in 1L distill Water
Chloroamine : 4mg/L in 1L distill Water
Florides : 0.5mg/L + in 1L distill Water
Copper : 0.005mg/L + in 1L distill Water
Lead : 1.3 mg/L in 1L distill Water

It should be sufficient to specify;
Chlorine : 4mg/L
Chloroamine : 4mg/L
Florides : 0.5mg/L
Copper : 0.005mg/L
Unless you actually meant mixing the 5 samples to make 5 litres of distilled water, which will dilute the concentration per litre in the final mix.

The temperature will be critical as it will change the density more than the dissolved species.

The speed of sound due to density can be calculated from;
Speed of sound, c = √ ( k / density );

Assume that for a density of 1.000000 the speed of sound is 1500 m/sec.
Then; 1500 = √ k ;
∴ k = 1500² = 2250000.

For the total dissolved species = 9.805 mg/litre;
c = √(2250000. / 1.009805);
∴ c = 1492.7 m/sec.

Gold Member
Unless you actually meant mixing the 5 samples to make 5 litres of distilled water, which will dilute the concentration per litre in the final mix.
The ambiguity did not escape me either.

Adding 4mL/L of Chloramine to a litre of pure water is not quiiiite the same thing as adding 4mL/L of Chloramine to a premade solution of 4mg Chlorine per litre of water.

Taking the OP at face-value, his/er method will end up with a volume of 1.01961L, whereas your method will lend up with a volume of 1.09805L, resulting in slightly different densities.

Either way, I'd still say we're talking on the order of 1 part in 10,000. At 1450m/s we're talking about less than 2cm/s difference in speeds. The distinction above brings that down almost another order of mag to mm/s.

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