Acoustics Problem #1 The steady-state response of a simple dynamic system to a sinusoidal excitation force is… F(t)=2.248sin(0.1πt)lbf and the resulting displacement response is: x(t)=0.328sin(0.1πt−30°)ft where the displacement lags the force by a phase angle ϕ=30°. Determine Solution Given Work done per cycle For harmonic excitation, the work done per cycle is Wcycle=πAF0sinϕ. Substitute A=0.328 ft, F0=2.248lbf, and sinϕ=sin(30°)=½: Wcycle= π(0.328)(2.248)(½)=1.159…

Symbol Description Units a speed of wave propagation; acceleration ft/s ; ft/s² A area ft² (or in²) A0 amplitude of wave ft (or in) A, B constants — c damping coefficient lbf·s/ft C, D constants — d diameter ft (or in) f frequency Hz (cycles/s) fb beat frequency Hz h length / height ft (or…

“The drag force, Fd, imposed by surrounding air on an automobile moving with velocity V is given by Fd = Cd · A · (1/2) · ρ · V2, where Cd is a constant called the drag coefficient. A is the projected frontal area of the vehicle, and ρ is the air density. For Cd = 0.45, A = 22½ ft2, and ρ = 1.23 ouncemass/ft3, calculate the power required (in hp) to…

“A classroom has a design sensible cooling load of 36,000 Btu/hr and a latent load of 12,000 Btu/hr at peak conditions. The room setpoint is 75 °F and the supply air temperature is 55 °F. Using standard air properties at sea level and the relations Qs=1.08×CFM×ΔT and 1 ton=12,000 Btu/hr, determine: (1) the required supply airflow (CFM) to handle the sensible load, (2) the total cooling capacity (tons),…

Mr. Rosenthal wants to save for a new Kia K5. He expects that it will cost $35 000 four and one-half years from now. How much money will he have to save each year and deposit in a savings account that pays 6⅓% per year, compounded annually, to buy the car in four and one-half…

“A small roadway project consists of the following activities:” Activity Duration (days) Predecessor(s) A 4 – B 6 A C 3 A D 5 B, C E 2 C F 4 D, E “Determine the critical path and total project duration using the Critical Path Method (CPM).” Step 1: Compute early start (ES) and early finish (EF) for…

Specific Gas Constant for Dry Air (Rair) — Imperial Unit Variants Length Force Mass Temp Rair (value) Units ft lbf lbm °R 53.35 ft·lbf/(lbm·°R) ft lbf slug °R 1716 ft·lbf/(slug·°R) ft poundal lbm °R 1.657 ft·poundal/(lbm·°R) ft poundal slug °R 5.52×104 ft·poundal/(slug·°R) ft kipf lbm °R 0.05335 ft·kipf/(lbm·°R) ft kipf slug °R 1.716 ft·kipf/(slug·°R) yd…

Question (Materials — Composites). A unidirectional carbon/epoxy lamina has fiber volume fraction Vf=0.60. The fiber modulus is Ef=33 Msi and the matrix modulus is Em=0.50 Msi. Assuming the rule of mixtures, find the longitudinal modulus E1 and the transverse modulus E2. Relations. Matrix fraction: Vm=1−Vf=0.40.Longitudinal (Voigt): E1=VfEf+VmEm.Transverse (Reuss): E2=(VfEf+VmEm)−1. Compute.E1=(0.60)(33)+(0.40)(0.50)=19.8+0.20=20.0 Msi.E2=(0.6033+0.400.50)−1=(0.01818+0.80)−1=(0.81818)−1=1.22 Msi. Answer. E1≈20.0 Msi, E2≈1.22 Msi (most nearly).

“A steam locomotive consumes feedwater at 120  galmi on level track. The scheduled run is 75 mi, and the tender holds 8,000 gal when full. Will one tender fill cover the run? If not, how many gallons short?” Total water needed:  120galmi×75mi=9,000gal. Shortfall:  9,000−8,000=1,000gal. Answer: No; it’s short by 1,000 gal (needs a water stop).

“An aircraft flying at an altitude where the air density is 0.00238 slugft³ has a wing area of 280 ft² and a lift coefficient (CL) of 0.45. What is the lift force (lb) when the aircraft speed is 200 ft/s?” The lift equation for an aircraft is: L=0.5×ρ×V2×S×CL Now plug in: L = 0.5 × (0.00238 slug/ft³)…