Question

When sound travels through the ocean, where the bulk modulus is 2.34 x 10^9 N/m^2, the wavelength associated with 1000.0 Hz waves is 1.51 m. 1) Calculate the density of seawater. (Express your answer to three significant figures.)

Answer 1

1.03×10³ kg/m³

Step-by-step explanation:

β = Bulk modulus = 2.34×10⁹ N/m²

f = Frequency = 1000 Hz

λ = Wavelength = 1.51 m

ρ = Density

Speed of the wave

v = fλ

⇒v = 1000×1.51

⇒v = 1510 m/s

Speed of sound

`v=\sqrt{(\beta)/(\rho)}\\\Rightarrow \rho=(\beta)/(v^2)\\\Rightarrow \rho=(2.34* 10^9)/(1510^2)\\\Rightarrow v=1026.27\ kg/m^3`

Density of seawater is 1.03×10³ kg/m³ or 1.03 g/cm³ (rounding)