Answer:
a) 107.1875 Hz
b) 214.375 Hz
c) 321.5625 Hz
Explanation:
L = length of the open organ pipe = 1.6 m
v = speed of sound = 343 m/s
f = fundamental frequency
fundamental frequency is given as
inserting the values
Hz
b)
first overtone is given as
f' = 2f
f' = 2 (107.1875)
f' = 214.375 Hz
c)
first overtone is given as
f'' = 3f
f'' = 3 (107.1875)
f'' = 321.5625 Hz
We have that the spring constant is mathematically given as
Generally, the equation for angular velocity is mathematically given by
Where
k=spring constant
And
Therefore
Hence giving spring constant k
Generally
Mass of earth
Period for on complete resolution of Earth around the Sun
Therefore
In conclusion
The effective spring constant of this simple harmonic motion is
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To solve this problem we will apply the concepts related to the calculation of the speed of sound, the calculation of the Mach number and finally the calculation of the temperature at the front stagnation point. We will calculate the speed in international units as well as the temperature. With these values we will calculate the speed of the sound and the number of Mach. Finally we will calculate the temperature at the front stagnation point.
The altitude is,
And the velocity can be written as,
From the properties of standard atmosphere at altitude z = 20km temperature is
Velocity of sound at this altitude is
Then the Mach number
So front stagnation temperature
Therefore the temperature at its front stagnation point is 689.87K