1soln1 - Physics 315 Oscillations and Waves Homework 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 315: Oscillations and Waves Homework 1: Solutions 1. The body will fly off the diaphragm whenever the diaphragm’s downward acceleration exceeds the acceleration, g , due to gravity. Hence, as the fre- quency increases, the body will first fly off the diaphragm when the maxi- mum downward acceleration becomes equal to g : i.e. , ω 2 a = g, Here, ω = 2 π f is the diaphragm’s angular frequency of oscillation, f is the same frequency in hertz, and a is the amplitude of the oscillation. It follows that f = 1 2 π radicalbigg g a . However, a = 1 × 10- 5 m and g = 9 . 8 m s- 1 , so f = 157 . 6 Hz. 2. Let A be the cross-sectional area of the body, V its volume, x its submerged depth, ρ its density, and ρ the density of the liquid. The submerged volume is V s = x A . According to Archimedes’ Principle, the buoyancy force is the weight of the displaced fluid. Hence, f B = ρ V s g = ρ A g x. The mass and weight of the body are ρ V and f W = ρ V g, respectively. Hence, the body’s equation of vertical motion is ρ V ¨ x = f W − f B = ρ V g − ρ A g x. In equilibrium, x = x , where x = ρ V ρ A . Let x = x + δx , where | δx | ≪ x . It follows, from expansion of the equation of motion to first-order in small quantities, that ρ V δ ¨ x = − ρ A g δx....
View Full Document

{[ snackBarMessage ]}

Page1 / 6

1soln1 - Physics 315 Oscillations and Waves Homework 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online