When you hear a noise, you usually know the direction from which it came even if you cannot see the source. This ability is part
ly because you have hearing in two ears. Imagine a noise from a source that is directly to your right. The sound reaches your right ear before it reaches your left ear. Your brain interprets this extra travel time (Δt) to your left ear and identifies the source as being directly to your right. In this simple model, the extra travel time is maximal for a source located directly to your right or left (Δt = Δtmax). A source directly behind or in front of you has equal travel time to each ear, so Δt = 0. Sources at other locations have intermediate extra travel times (0 ≤ Δt ≤ Δtmax). Assume a source is directly to your right.(a) Estimate the distance between a person's ears. (they gave us the answer of .2... apparently the program is messed up and we have to use .2(b) If the speed of sound in air at room temperature is vs = 338 m/s,find Δtmax. (Use your estimate.)
(c) Find Δtmax if instead you and the source are in seawater at the same temperature, where vs = 1534 m/s. (Use your estimate.)
(c) Find Δtmax if instead you and the source are in seawater at the same temperature, where vs = 1534 m/s. (Use your estimate.)
1 answer:
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Answer:
v = (-4.44 i^ + 6.66 j^ ) m/s, a_average =( 0 i^ -2π j^) m/s²
Explanation:
The expression left corresponds to an oscillatory movement (MAS), the speed is defined by
v = dr / dt
the function of position
r = 2 cos πt i^ + 3 sin πt j^
let us note that it is a movement in two dimensions
let's perform the derivative
v = -2π sin πt i^ + 3π cos πt j^
we evaluate this expression for t = 0.25 s, remember that the angle is in radians
v = -2π sin (π 0.25) i^ + 3π cos (π 0.25) j^
v = (-4.44 i^ + 6.66 j^ ) m/s
To calculate the mean acceleration we use the expression
a = () / Δt
indicates that the time is the first 3 s
we look for the initial velocity t = 0 s
v₀ = 0 i ^ + 3π j ^
we look for the fine velocity, t = 3 s
v_f = - 2π sin (π 3) + 3π cos (π 3) j ^
v_f = 0 i ^ - 3π j ^
we calculate the average acceleration
Δt = (3 -0) = 3 s
a_average = (0-0) / 3 i ^ + (-3π - 3π) / 3
a_average = (0 i ^ -2π j ^ ) m/s²