Atube, open at only one end, is cut into two shorter (non-equal) lengths. the piece open at both ends has a fundamental frequency of 425 hz, while the piece open only at one end has a fundamental frequency of 675 hz, both in room temperature air. what is the fundamental frequency of the original tube?

f= 158.6Hz

Explanation

Given Data

f₀=425 HzOpen at both ends has a fundamental frequency

f₁=675 Hzopen only at one end has a fundamental frequency

To find

Fundamental frequency of the original tube

Solution

Fundamental frequency with open ends given as

f = v / (2·L)

where v speed of sound,

and  L is length

And

Fundamental frequency of a tube closed at one end is given as

f = v / (4·L)

For the piece with two open ends:

f₀ = v / (2·L₀)

L₀ = v / (2·f₀)

For the other piece

f₁ = v / (4·L₁)

L₁ = v / (4·f₁)

The fundamental frequency of the original tube is that of a closed end tube of length L₀+ L₁.

f = v/ ( 4·(L₀+ L₁)

f= v/ (4·(v / (2·f₀)+ v / (4·f₁) )

f= 1/ ( 2/f₀+ 1/f₁)  

f= 1/ ( 2 / 425Hz + 1 / 625Hz)

f= 158.6Hz

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.