Answer:
Explanation:
Given
Lowest four resonance frequencies are given with magnitude
50,100,150 and 200 Hz
The frequency of vibrating string is given by
where n=1,2,3 or ...n
L=Length of string
T=Tension
Mass per unit length
When string is clamped at mid-point
Effecting length becomes 
Thus new Frequency becomes
i.e. New frequency is double of old
so new lowest four resonant frequencies are 100,200,300 and 400 Hz
Answer:
C. community
Explanation:
Community consists of a local residence, like a town.
| Impedance | = √ [R² +(ωL)²]
R² = 6800² = 4.624 x 10⁷
(ωL)² = (2 · π · f · 2.3 · 10⁻³)²
= 2.0884 x 10⁻⁴ f²
| Z | = √[ (4.624 x 10⁷) + (2.0884 x 10⁻⁴ f²) ] = 1.6 x 10⁵
(1.6 x 10⁵)² = (4.624 x 10⁷) + (2.0884 x 10⁻⁴ f²)
(2.56 x 10¹⁰) - (4.624 x 10⁷) = 2.0884 x 10⁻⁴ f²
Frequency² = (2.56 x 10¹⁰ - 4.624 x 10⁷) / 2.0884 x 10⁻⁴
= 2.555 x 10¹⁰ / 2.0884 x 10⁻⁴
= 1.224 x 10¹⁴
= 122,400 GHz <== my calculation
11.1 MHz <== online impedance calculator
Obviously, I must have picked up some rounding errors
in the course of my calculation.
Answer:
Δv = 12 m/s, but we are not given the direction, so there are really an infinite number of potential solutions.
Maximum initial speed is 40.6 m/s
Minimum initial speed is 16.6 m/s
Explanation:
Assume this is a NET impulse so we can ignore friction.
An impulse results in a change of momentum
The impulse applied was
p = Ft = 1400(6.0) = 8400 N•s
p = mΔv
Δv = 8400 / 700 = 12 m/s
If the impulse was applied in the direction the car was already moving, the initial velocity was
vi = 28.6 - 12 = 16.6 m/s
if the impulse was applied in the direction opposite of the original velocity, the initial velocity was
vi = 28.6 + 12 = 40.6 m/s
Other angles of Net force would result in various initial velocities.
