You have your headphones turned all the way up (100 dB). a. If you want them to sound half as loud, to what decibel level must the music be set?

b. If you want them to sound 1/4 as loud, to what decibel level must the music be set?

a. 90 dB

b. 80 dB

Explanation:

The given parameter of the sound is as follows;

The level to which the headphones are tuned = All the way up

The intensity of the sound of the headphones when tuned all the way up = 100 dB

a. The relationship between level change in loudness, ΔL, and the ratio of loudness, 'x', is presented as follows;

ΔL = 10·log₂(x) ≈ 33.22·log(x)

Therefore, for a sound to be half as loud, we have x = 1/2, therefore;

ΔL = 10·log₂(1/2) = 10·log₂(2⁻¹) = -10 ≈ 33.22·log(1/2)

The change in the intensity level for a sound half as loud, ΔL = -10 dB

Given that the sound was initially at 100 dB, the new level for a sound half as loud = 100 dB + ΔL = 100 dB - 10 dB = 90 dB

The decibel level the music must be set for a sound half as loud = 90 dB

b. In order for the sound to be 1/4 as loud, we have;

ΔL = 10·log₂(1/4) = 10·log₂(2⁻²) = -20

Therefore, the change in the level of the sound intensity level, ΔL by -20 dB will given a sound that is 1/4 as loud

The initial intensity level = 100 dB

The intensity level for a sound 1/4 as loud = 100 dB - 20 dB = 80 dB

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.

i dont think you are wrong for wanting to get even with someone who did you wrong.

(i'm an eye for an eye kind of person) but if this person hurt you in a sexual way, i dont suggest doing anything to him. he should be taken to the proper authorities, you could go to jail depending on what you do. if it was something small like your sibling took your spot on the couch, than yea, i would get even with him by taking one of his favorite snacks lol. but i dont suggest you doing anything illegal.