Physics: When you blow across the top of asoda bottle, it acts like a closed pipewith a fundamental frequency of495 Hz. If you pour 0.030 m of waterinto the bottle, shortening the air cavity,what is the new fundamental frequency?(Hint: Find the original length.)(Speed of sound = 343 m/s)(Unit = Hz)

A Explanation: Correct on A P E X...

When you blow across the top of asoda bottle, it

Geo777

19.01.2022

The new fundamental frequency will be 598.7Hz.

Explanation:

The fundamental wavelength of the sound waves in the soda bottle is given by the equation

$\lambda = \dfrac{v}{f}$

where is the speed of sound, and is the frequency. Since f = 495Hz and v = 343m/s , we have

$\lambda = \dfrac{343m/s}{495Hz}$

$\boxed{\lambda = 0.693m.}$

Because it is a fundamental wavelength, the length of the soda can must be

$L = \dfrac{\lambda}{4}$

$L = \dfrac{0.693}{4}$

$\boxed{L = 0.173m}$

The length of the soda bottle is 0.173 meters.

Now, if we pour 0.030 m of water, the new length of the air cavity becomes $L_{new}=0.173m-0.03m$

$L_{new} = 0.143m$

Therefore, the new fundamental wavelength will be

$\lambda_{new} = 4L_{new}$

$\lambda_{new} = 0.573m$ ,

which is a frequency of

$f_{new} = \dfrac{343m/s}{0.573m}$

$\boxed{ f_{new} = 598.7 Hz.}$

Thus, the new fundamental frequency is 598.7Hz.

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