time period of oscillation & wavelength of disturbance

Question

If the velocity of a disturbance in a steel rod is 2000 m/s & the frequency of vibration is 2000 Hz, find a) the time period of oscillation of each particle of the rod b) wavelength of the disturbance & c) density of the rod. And given is young's modulus of elasticity = 11 x 10^10 n/m^2.

 

Ok, so I think I figured out a), could you please confirm? Since we have velocity & frequency I calculated T = 1/f = 0.0005 s

Now I am struggling w b) & c). I believe the correct formula for wavelength is: lambda = v/f, but that answer is 1 & makes no sense & it also makes no sense that I have young's modulus & haven't incorporated it into my calculations. I have also got v= root of young's modulus / density. Density is defined as mass / volume. I am stuck, where do I take mass & volume from? I feel like it's so simple I am just not seeing the answer.

 

Help please?

Thanks

Answer 1

(a) and (b)

 

Your calculations of period and wavelength are both correct for the given information.  Lambda = 1 m.

 

(c)

 

You are correct that v = sqrt(Y / rho)

 

Y is given as 11 x 10^10 N/m^2

 

rho = Y / v^2 = (11 x 10^10 N/m^2) / (2000 m/s)^2 = 27500 kg/m^3