Understanding Sound Wave Amplitude in the Equation s=Sm cos(kx-wt)

In summary: Solid, liquid, and gas have different types of waves that can propagate through them. Mechanical waves, such as longitudinal waves in a rope, can only propagate through solid media.
  • #1
elabed haidar
135
1
i have a question about sound waves :
we know that the equation of sound wave can be written in the form s=Sm cos(kx-wt)
,but i still don't get the meaning of Sm .I know that in the transverse wave ingeneral , and in particular the string the maximum amplitude is how much the string can go vertically upward ,
so what about the maximum amplitude in sound wave?
PS the defintion of sound wave amplitude is the maximum postion of the element at equilibrium ?
 
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  • #2
hi elabed haidar! :smile:

as you know, s is displacement and sm is maximum displacement …

the displacement here is the distance any particular particle goes from its own equilibrium position …

in a transverse wave it goes up or down, and in a spring (or sound wave) it goes forward and backward :wink:
elabed haidar said:
PS the defintion of sound wave amplitude is the maximum postion of the element at equilibrium ?

you mean the maximum postion of the element from its equilibrium position?

yes, the maximum distance forward or backward :smile:
 
  • #3
i still don't get it can you please illustrate more please?
 
  • #4
here is the problem i understand it in a spring Xm but in a sound wave i still don't get it
 
  • #5
one more thing in sound wave resonance why when we have tube which is one open from only one side the resonant frequency f=nv/4 lamda ?? and thank you very much professor
 
  • #6
for pictures, google "longitudinal wave" and click "Images" :smile:
 
  • #7
why does longitudinal waves can propagate through solid, liquid and gas? and not transverse except in solid?
 
  • #8
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  • #9
elabed haidar said:
one more thing in sound wave resonance why when we have tube which is one open from only one side the resonant frequency f=nv/4 lamda ?? and thank you very much professor

Because the open end will have an antinode at it and you can't just have any wavelength because antinodes occur periodically
 
  • #10
chrisbaird said:
Sound waves are pressure waves, so the picture of a longitudinal wave going down a spring is not always helpful. The amplitude of the sound wave is the maximum local air pressure reached when the wave traverses through it. So a sound wave with a higher amplitude (a louder sound) will have higher pressure. http://www.dailymotion.com/video/x6bz5x_plane-breaks-sound-barrier-then-exp_tech"
but how does mechanical longitudinal wave travel in solid, liquid and gas medium? and transverse mechanical wave (such as in rope)travels only in solid medium?
 
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  • #11

1. What does the equation s=Sm cos(kx-wt) represent?

The equation s=Sm cos(kx-wt) represents a sound wave in a medium, where s is the displacement of the medium, Sm is the maximum displacement, k is the wave number, x is the position, w is the angular frequency, and t is the time.

2. How does the amplitude affect the sound wave?

The amplitude, represented by Sm in the equation, determines the maximum displacement of the medium. A larger amplitude results in a louder sound, while a smaller amplitude produces a softer sound.

3. What is the relationship between the amplitude and the energy of the sound wave?

The amplitude and energy of a sound wave are directly proportional. This means that as the amplitude increases, so does the energy of the sound wave.

4. How does the frequency of the sound wave affect the amplitude?

The frequency, represented by k in the equation, does not directly affect the amplitude of the sound wave. However, it does affect the wavelength and speed of the wave, which in turn can affect the amplitude.

5. Can the amplitude of a sound wave be negative?

Yes, the amplitude of a sound wave can be negative. This means that the wave is traveling in the opposite direction and has a displacement in the opposite direction of the original wave.

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