Longitudinal waves in a quartz plate

[Karol]

Homework Statement

In a quartz longitudinal waves produce peaks on the 2 sides of the plate. the base frequency is:
$f_1=\frac{2.87E5}{s}$
Where s is the thickness. calculate Young's modulus of quartz.
$\rho$=specific mass=2.66[gr/cm³]

Homework Equations

$\lambda$=wavelength, u=velocity $\lambda=\frac{u}{f}$
E=young's modulus, $u=\sqrt{\frac{E}{\rho}}$

The Attempt at a Solution

I need to find the velocity u, but it depends on the length of the plate which i don't have. and even if i have the length, the frequency depends on the thickness. but since there is one Young modulus, since i was asked about, then there is one velocity.
If i write Young's modulus and the specific mass in their ingredients then the length cancels but then i have 3 other variables. and besides i am given $\rho$.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[nasu]

You can express the wavelength as a function of s, the thickness of the plate.

 

[Karol]

Yes, i can express the wavelength as a function of the thickness s but not as a function of the length hence i get many velocities u hence i cannot get one young's modulus E

 

[nasu]

What length?

And you don't get many velocities. They tell you that f is the base frequency. So you can find the base wavelength corresponding to maxima on the two faces (2s). And then the velocity.

 

[Karol]

Oh, now is see what you mean, i thought of the length as the long dimension of the plate, which is unknown, i will try to solve now