need a good grade on test, please be fast and accurate :D 1. An open cylindrical

Question

need a good grade on test, please be fast and accurate :D

1. An open cylindrical container with very large radius is at rest a distance H above the ground at the edge of a platform. A tiny hole develops at the bottom of the container and water from the container squirts out horizontally landing a distance H from the edge of the platform. For the water to land at this location, what is the ratio of the depth of the water L in the container to H?

2. A tube of air open at only one end is vibrating in the 7th harmonic from a tuning fork of frequency 91 Hz placed at the open end. If this tube of air were to vibrate at its fundamental frequency, what frequency, in Hz, tuning fork would be needed at the open end?

4. Given a wave produced by a simple harmonic oscillator whose displacement in meters is given by the equation

Explanation / Answer

1) v = sqrt(2*g*L)

let t is the time taken to fall on ground


H = 0.5*g*t^2

t = sqrt(2*H/g)

so, H = v*t = sqrt(2*g*L)*sqrt(2*H/g)

H = 2*sqrt(H*L)

H^2 = 4*H*L

==> L/H = 1/4

2) f7 = 13*fo

fo = f7/13 = 91/13 = 7 Hz

3)

f' = (340/340-30)*1000 = 1096.77 Hz

4)


w = 12 rad

f = w/2*pi = 1.91 HZ

5)

0.5*k*x^2 = 20

k = 20*2/0.5^2 = 160 N/m

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