How does tension affect wave speed in different mediums?

[astro_kat]

Hi all,
my high school physics class has been concerned with waves for some time now. Hoever, we've only considered waves/pulses in strings and cprings, solid mediums anyways. Our textbook has an advanced problem section that asks a bunch about waves in liquid and gaseous mediums--such as a dolphin using sonar in water, sending an echo, which will return. Or sound waves in air. I'm really confused how to approach these problems.

Another problem is guitar strings, when they give me the mass and or volume to solve for the wavelength, wavespeed, frequency, and time to reflect...

There has to be some relation between density, tension, and waves/pulses. Can anyone point me in the right direction.

*If anyone can suggest a practice problem and show me how to solve it (a rather hard one please) I'd much appreciate it. I really have no idea what's going on in physics anymore, all help will eb appreciated!

 

[Kurdt]

Hyperphysics is always a good place to start.

http://hyperphysics.phy-astr.gsu.edu/Hbase/sound/trawvcon.html#c1

And yes there is a relation between the tension density and wave speed for a stretched string.

Wave speed is: $$v=\sqrt{\frac{T}{\mu}}$$

where $\mu$ is the mass per unit length.

 

[astro_kat]

ok, that's cool, but what is the *mass/unit of length* measured in? Kg/m, g/cm, does it matter what units I use?

 

[Kurdt]

The standard SI units would be kg/m. Since tension is invariably given in Newtons it would just complicate it unnecessarily to use any others. In my opinion.

 

[astro_kat]

oh yeah, I found something in my friend's college textbook, saying that:

F(t) = (delta L)/(initial L) * E * A

in other words, (tension) equals (Elastic modulus) times (strain) times (area).

I guess that's how I'd find the tension, but what of waves in water, they kinda confuse me. Like an echo, how long it takes to hit the wall and come back. My teacher said I needed to know the density of sea water and do something with that. Any ideas?

 

[Kurdt]

Sound waves in fluids and solids have a speed that depends on the mediums bulk modulus and the density. The equation will look familiar.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html

 

[astro_kat]

oh, OK thanks a bunch!

 

[astro_kat]

so, that's all been very helpful... but how does tension relate to the wave equation:
V = wavelength * frequency)