Quiz - Physics - Sound

[Pedro Burrito]

From the PADI Dive Theory Exam:

Sound travels ____ times faster in water than in air because water is so much ____ than air.

a. twenty / denser

b. two / warmer

c. four / colder

d. four / denser


I will post a daily question from my exams to help newer divers and to encourage more experienced divers to interact gracefully and helpfully with the newer divers.

Reminder - this is a post in the Basic Forum and it is a green zone. Please be nice and on topic.

Thank you for your patience while we try to give people something to discuss other than Covid-19 and/or Politics. I will post the answer covered by the spoiler tag later today.

 

[Ukmc]

I don’t think there will be a lot of controversy on this question . However, a good test taker could figure this question out without any knowledge of physics

 

[Angelo Farina]

Actually all answers are wrong.
The speed of sound in a liquid, c, is given by the square root of the bulk modulus (aka stiffness coefficient) K divided by the density ρ, as described by the Newton-Laplace equation:

Hence increasing the density makes the sound speed TO DECREASE!
The sound speed in water is larger than in air because water is much more stiff than air (which is highly compressible), not because water is more dense...

 

[Angelo Farina]

Actually all answers are wrong.
The speed of sound in a liquid, c, is given by the square root of the bulk modulus (aka stiffness coefficient) K divided by the density ρ, as described by the Newton-Laplace equation:
View attachment 581401
Hence increasing the density makes the sound speed TO DECREASE!
The sound speed in water is larger than in air because water is much more stiff than air (which is highly compressible), not because water is more dense...

Said that, one could expect that the sound speed is lower in salt water as it is more dense than fresh water. And instead, the sound speed in salt water is larger...
So what?
Read here for an explanation, but making it short, the effect of salt is larger on increasing the bulk modules K than on increasing density ρ!
Why does sound travel faster in Salt water then fresh water? : askscience

 

[scubadada]

Actually all answers are wrong.
The speed of sound in a liquid, c, is given by the square root of the bulk modulus (aka stiffness coefficient) K divided by the density ρ, as described by the Newton-Laplace equation:
View attachment 581401
Hence increasing the density makes the sound speed TO DECREASE!
The sound speed in water is larger than in air because water is much more stiff than air (which is highly compressible), not because water is more dense...

Ha, I was expecting this

 

[Steve_C]

Knowing it travels faster and further in water, salt or fresh, is the useful information.

 

[rhwestfall]

and so it begins...

 

[Angelo Farina]

Knowing it travels faster and further in water, salt or fresh, is the useful information.

Faster does not necessarily means that sound travels further. It travels in water for hundredths of kilometres not due to the large sound speed, but due to two concurring factors:
1) The mechanical losses are very very small, so a very tiny amount of acoustical energy is converted to heat.
2) Sound does not spread vertically, as the vertical gradients of temperature and salinity create what is called a "sound channel" (SOFAR channel), so the energy is confined at intermediate depth without ever hitting the surface or the sea bottom.

More info: NOAA Ocean Explorer: Sounds in the Sea 2001: diagram of how sound travels underwater

Knowing that the sound speed in water is larger than in air is important for the diver for another reason: we localise the direction of arrival of sound hitting our ears by means of two "cues", inter-aural time difference (ITD) at low frequency and inter-aural level difference (ILD) at high frequency.

ITD effect (left), ILD effect (right)
​

If sound travels faster, of course the inter-aural time difference between the two ears is strongly reduced. Furthermore, if the sound speed is larger, also the wavelength becomes larger, hence the human head does not provide anymore a significant shadow effect, and also the inter-aural level difference is much smaller than in air.
So we lose both cues, when being underwater, and we cannot localise anymore where the sound is coming from.
There are technologies which allow to retrieve directional hearing underwater, but I suppose that presenting them here would be overkilling, as we are in the "basic" section...
Instead all what I wrote in this thread is something which has been taught to my sons at the beginning of secondary school, when they were eleven or twelve, hence I consider this to be "basic science".

 

[BlueTrin]

I don’t think there will be a lot of controversy on this question .

I am sure we will find a way to argue about the solutions

 

[Angelo Farina]

I am sure we will find a way to argue about the solutions

That is the effect of being locked at home with nothing to do since more than 5 weeks!