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Alex787 [66]
3 years ago
12

In Trial III, a different, looser, spring is used; its force constant is 23.1 N/m. The suspended mass is the same as the one in

Trial I: 0.400 kg. Theoretically speaking, what period of oscillations should we expect, based on these values of k and m? Enter your answer in seconds with two significant figures.
Physics
1 answer:
cricket20 [7]3 years ago
7 0

Answer:

T=0.827s

Explanation:

The period of a spring can be calculated with the equation

T=2\pi w

But we know as well that w is given by,

w=\sqrt{\frac{k}{m}}

Replacing,

w=\frac{2\pi}{T}= \sqrt{\frac{k}{m}}\\T=2\pi\sqrt{\frac{k}{m}}\\T=2\pi\sqrt{\frac{0.4}{23.1}}

So we have that

T=0.827s

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Answer:

L=0.654 m

Explanation:

<u>Concepts and Principles  </u>

1- The speed of sound in air is expressed as a function of the temperature of air as follows:  

 v=(331 m/s)√(1+T_C/273°C)                        (1)

where 331 m/s is the speed of sound in air at temperature 0°C and Tc is the temperature of air in Celsius.  

<u>Standing Wave Patterns in Pipes:  </u>

A pipe open at both ends can have standing wave patterns with resonant frequencies:  

f=v/λ=nv/2L                     n=1,2,3.........

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<u>Given Data </u>

f_1 (fundamental frequency of the flute) = 262 Hz

T (temperature of the air) = 20°C  

The flute is open at both ends.  

<u>Required Data </u>

We are asked to determine the length of the tube.  

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The speed of sound in air at temperature T = 20°C is found from Equation (1):

 v=(331 m/s)√(1+T_C/273°C)  

 =342.91 m/s

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f=v/2L

Solve for L:  

L=v/2f_1

L=0.654 m

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