Question

(a) In a liquid with density 1300 kg //m^(3) , longitudinal waves frequency 400 H_(Z) are found to have wavelength 8.00 m . Calculate the bulk modulus of the liquid. (b) A metal bar with a length of 1.50 m has density 6400 kg//m^(3) . Longitudinal sound waves take 3.90xx10^(-4) s to travel from one end of the bar to the other. What is young's modulus for this metal?

Answer 1

Thus the young's modulus of this metal is Y = 9.47 × 10^10 N/m^2

Explanation:

(a) ν = fλ  = √  B / ρ

B = ρ(fλ)^2

B = (1300) (400 × 82)

= 1.33 x 10^10 N/m^2

(b) ν = l / t = √ Y / ρ

∴Y = ρ(l / t)^2 = (6400) (1.5)3.9×10−4)^2

= 9.47 × 10^10 N/m^2

Thus the young's modulus of this metal is Y = 9.47 × 10^10 N/m^2