When you blow across the top of a soda bottle, it acts like a closed pipe with a fundamental frequency of 495 Hz. If you pour 0.030 m of water into the bottle, shortening the ai…

Question

asked Feb 19, 2021 80.4k views

2 Answers

Jordan Stewart · Answer 1 · 2021-02-24T21:31:26+0000

Answer:

The new fundamental frequency will be 598.7Hz.

Step-by-step explanation:

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

$\lambda = (v)/(f)$

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

$\lambda = (343m/s)/(495Hz)$

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

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

$L = (\lambda)/(4)$

L = (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) = (343m/s)/(0.573m)

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

Thus, the new fundamental frequency is 598.7Hz.