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SVETLANKA909090 [29]
3 years ago
6

The 2779-m Brooklyn-Battery Tunnel, connecting Brooklyn and Manhattan, is one of the world's longest underwater vehicular tunnel

s. (a) Determine its fundamental frequency of vibration. (b) What harmonic must be excited so that it resonates in the audio region at 20 Hz or greater?
Physics
1 answer:
Marina CMI [18]3 years ago
3 0
For a cylinder that has both ends open resonant frequency is given by the following formula:
f= \frac{nv}{2L}
Where n is the resonance node, v is the speed of sound in air and L is the length of a cylinder.
The fundamental frequency is simply the lowest resonant frequency.
We find it by plugging in n=1:
f_0= \frac{v}{2L}=\frac{343}{2\cdot 2779}=0.062 Hz
To find what harmonic has to be excited so that it resonates at f>20Hz we simply plug in f=20 Hz and find our n:
20= \frac{n343}{2\cdot 2779} =n\cdot f_0
We can see that any resonant frequency is simply a multiple of a base frequency.
Let us find which harmonic resonates with the frequency 20 Hz:
20=n\cdot f_0\\ n=\frac{20}{0.062}=322.58
Since n has to be an integer, final answer would be 323.

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Momentum = (mass) x (velocity)

Original momentum before the hit =

                   (0.16 kg) x (38 m/s) this way <==

               =             6.08 kg-m/s  this way <==

Momentum after the hit =

                   (0.16) x (44 m/s) that way  ==>

               =           7.04 kg-m/s  that way ==>

Change in momentum = (6.08 + 7.04) =  13.12 kg-m/s  that way ==> .
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Change in momentum = impulse.

                                   Impulse = (force) x (time the force lasted)

                          13.12 kg-m/s  = (force) x (0.002 sec)

  (13.12 kg-m/s) / (0.002 sec)  =  Force

             6,560 kg-m/s² = 6,560 Newtons  =  Force   

                            ( about 1,475 pounds  ! ! ! )
8 0
3 years ago
You push against a wall and the wall pushes back on you.
emmainna [20.7K]

Answer:

Its the third law of motion.

Explanation:

Newton's third law of motion states that every action has equal and opposite reaction.

4 0
3 years ago
A gray kangaroo can bound across level ground with each jump carrying it 9.1 m from the takeoff point. Typically the kangaroo le
Alona [7]

Answer:

u = 10.63 m/s

h = 1.10 m

Explanation:

For Take-off speed ..

by using the standard range equation we have

R = u² sin2θ/g

R = 9.1 m

θ = 26º,

Initial velocity = u

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u² = \frac{Rg}{sin2\theta}

u^2 = \frac{9.1 x 9.80}{sin26}

u^2 = 113.17

u = 10.63 m/s

for Max height

using the standard h(max) equation ..

v^2 = (v_osin\theta)^2 -2gh

h =\frac{(v_o^2sin\theta)^2}{2g}

h  =  \frac{(113.17)(sin26)^2}{(2 x 9.80)}}

h = 1.10 m

7 0
3 years ago
A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axi
Lubov Fominskaja [6]

Answer:

The moment of inertia is I=\frac{M}{12} a^{2}

Explanation:

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I=\int\limits^a_b {r^{2}\frac{M}{a}  } \, dr\\a=\frac{a}{2} \\b=-\frac{a}{2}

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7 0
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True or false? If two components are connected in series, the current through one component will
Molodets [167]

the answer is ( True ) .

the current is the same in series circuits .

8 0
3 years ago
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