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

Answer:

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

Answer 2

Answer:

598.7 Hz

Explanation: