Question

An open vertical tube has water in it. A tuning fork vibrates over its mouth. As the water level is lowered in the tube, the seventh foss (zef86) – Homework 10, oscillations and waves 19-20 – dowd – (PriceEPHY11920 2) 5 resonance is heard when the water level is 55.25 cm below the top of the tube. 55.25 cm What is the wavelength of the sound wave? The speed of sound in air is 343 m/s. Answer in units of cm

Answer 1

Wavelength = 17cm

Frequency = 2017.65 s^(-1)

Step-by-step explanation:

A) Standing wave is the result of superposition of two identical waves with only the difference being that they travel in opposite directions to each other.

Now, quarter wavelength transmission line, the number of quarter wavelengths in the length of the pipe is given as;

J = 2N - 1

Where N is the number of nodes in the air column.

Question says the 7th resonance is heard at that water level, thus, N = 7

So, J = 2(7) - 1 = 14 - 1 = 13

Now, J is also expressed as, L/(λ/4)

Where L is the water level and λ is the wavelength.

From the question, L = 55.25 cm

Thus, L/(λ/4) = 13

Let's make λ the subject ;

λ = 4L/13

λ = (4 x 55.25)/13

λ = 221/13

λ = 17cm

Now, frequency is found from the formula ;

f = V/λ

From the question, v = 343 m/s

λ = 17cm = 0.17m

Frequency = 343/0.17 = 2017.65 s^(-1)

Answer 2

Answer / Explanation:

Referencing the diagram of a resonance in a vertical tube as illustrated in the attached diagram below,

we can say that:

Vertical wave is the result of superposition of dual and identical waves.

We should also note that the only difference is that they travel in opposite directions to each other.

So, let assume a tuning fork is vibrated with frequency ν at the open end of the tube of varying length which can be changed during vibration with the help of water level change.

Also, let us assume the minimum length of the tube be L, when the resonance is heard.

Also, we assume that 1/4 of the wavelength λ of the standing wave is equal to length of the minimum length L of the tube.

Hence, we have:

λ = 4 L .

So, if speed of sound in air is V , then frequency of the tuning fork can be expressed as:

U = v / λ = v / 4L

Noting that we have been given the speed of sound in air as V = 343 m / s .

where:

U = v / λ = v / 4L

therefore,

343 m / s / 4 x 0.5525 m

= 155.20 Hz

Noting that 1 wave length in centimeter is 29979245800 Hz

Therefore, I wavelength in centimeter = 29979245800 Hz / 155.20 Hz

= 193 cm