Question

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 air cavity,
what is the new fundamental frequency?
(Hint: Find the original length.)
(Speed of sound = 343 m/s)
(Unit = Hz)​

Answer 1

598.7 Hz

Step-by-step explanation:

Answer 2

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
`v` is the speed of sound, and
`f` 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
`L` 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.