The hot chocolate effect to investigate the effects on speed of sound

[Josielle Abdilla]

Summary:: The Hot chocolate effect is an investigation that extracts the essence about the effects on speed of sound. This is carried out in this sequence: A cup filled with liquid is continiously being tapped from the bottom. Meanwhile, a disturbance in the longitudinal sound waves is being caused by the formation of bubbes on adding hot chocolate powder

At first, the effective speed of sound decreases as hot chocolate powder is added. At which point does a standing wave is created, is it when the wave caused by the tappung sound reflects off the surface of liquid and interferes with the wave which has not yet reached the surface of the liquid.

a) According to my research, this is created when a note of frequency of a quarter of a wavelength is formed, what exacty does this mean and is frequency dependent on the depth of the cup?

b) Also, where is a displacement and pressure node is created?

c) When will the note with highest frequency be heard?
Thanks.. looking foward to help my out :)

 

[etotheipi]

I just had a go at this (you know, quarantine and all...) and was surprised that it actually worked (sort of)!

To me it seems this is essentially a half open pipe, where the base of the cup is the closed end and the surface of the liquid the open end. The lowest frequency standing wave you can produce indeed occurs when the wavelength is 4 times the height of the liquid. Sort of like:

When you stir the liquid you introduce more bubbles which alters the bulk modulus and consequently the speed of sound waves in the liquid. So for the same harmonic (depending on a given $\lambda$) you get a different $f$, and the note changes.

Something that can also be confusing is that a "pressure node" is equivalent to a "displacement anti-node", and vice versa. At the open end, the pressure is constant so this constitutes a node for pressure. At the closed end, the displacement of the medium is zero so this constitutes a node for displacement. Make sure to clarify which one you're talking about!

I also found this, which might be useful: https://www.epj-conferences.org/articles/epjconf/pdf/2014/04/epjconf_efm-13_02011.pdf

 

[Josielle Abdilla]

Thanks a lot. Much appreciated!

 

[Josielle Abdilla]

I have another question about the Young's double slit experiment, if you are interested:
Situation: Two parallel slits are illuminated by sodium light and observed by an observer looking through slit at a distance of 3m from the double sit. What can be observed when the slit separation in the double slit is reduced from 4mm wide to zero. I find this confusing since we always observe the fringes produced on a screen whereas in this situation the screen is replaced by an observer.
Thanks :)

 

[Josielle Abdilla]

Yes please that would be great and appreciated once again