How Does Liquid Volume in a Soda Bottle Affect the Sound Frequency Produced?

[ledzeppelinpa]

1. A child blows on a 20cm high soda bottle, and it creates a sound of 455Hz, how much liquid is inside the bottle?


2. not nsure about the equations



3. i attempted a solution, but all came out to something along the lines of 0.018

i don't think that's right

 

[ledzeppelinpa]

A child blows on a 20cm high soda bottle, and it creates a sound of 455Hz, how much liquid is inside the bottle?

Equation is 1/4*V*1/f = L

 

[Moetasim]

I would approach this problem by first understanding the relationship between the length of a tube and the frequency of sound it produces. In this case, the soda bottle acts as a closed tube and the child blowing into it creates a standing wave with a frequency of 455Hz. The fundamental frequency of a closed tube is given by the equation f = v/2L, where v is the speed of sound and L is the length of the tube.

To solve for the amount of liquid inside the bottle, we need to rearrange the equation to solve for L. This gives us L = v/2f. We know that the speed of sound in air is approximately 343 m/s. Substituting this value and the given frequency of 455Hz, we get L = 0.376 m.

However, this is the length of the entire bottle, including the neck. To find the length of just the liquid inside, we need to subtract the length of the neck, which is approximately 2 cm. This gives us a final length of 0.356 m for the liquid inside the bottle.

To convert this length to volume, we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius of the bottle and h is the length of the liquid inside. Assuming the bottle has a radius of 5 cm, the volume of liquid inside would be approximately 0.088 liters.

In conclusion, by understanding the relationship between tube length and frequency of sound, we can use mathematical equations to determine the amount of liquid inside the soda bottle. However, it is important to double check our calculations and assumptions to ensure accuracy.