A well with vertical sides and water at the bottom resonates at 7.00 H

Adela Brown

Adela Brown

Answered question

2022-01-05

A well with vertical sides and water at the bottom resonates at 7.00 Hz and at no lower frequency. The air-filled portion of the well acts as a tube with one closed end (at the bottom) and one open end (at the top).The air in the well has a density of 1.10×kgm3 and a bulk modulus of
1.33×105Pa
How far down in the well is the water surface?

Answer & Explanation

Annie Gonzalez

Annie Gonzalez

Beginner2022-01-06Added 41 answers

The water of the bottom resonates at 7 Hz 
The air in the well has a density of 1.1kgm3 a bulk modulus of 1.33×105Pa 
The frequency of water is given by 
f=vλ 
λ=4L, L is the depth of the well from the water surface to the open end at the top. 
L=v4f 
v=βρβ is the bulk modules, ρ is the density of air in the well 
L=14fβρ 
L=14×7Hz×1.33×105pa1.1kgm3 =12.4m (answer)

eninsala06

eninsala06

Beginner2022-01-07Added 37 answers

Both the top of the well and the top of the water are displacement nodes and anti-nodes, respectively. Exactly one-fourth of a wavelength may fit within the well's depth at the lowest resonance frequency.

If d is the depth and λ is the wavelength, then λ=4d

The frequency is f=vλ=v4d
Where v is the speed of sound. The speed of sound is given by v=βρβ is the bulk modulus ρ is the density of air in the well. Thus f=(14d)βρ and d=14fρβ
=14(7.00Hz)1.33×105Pa1.10kgm3=12.4m

karton

karton

Expert2022-01-11Added 613 answers

One might imagine the well as an open organ pipe. The formula for its fundamental frequency is
n=v41 and v=βρ n=βρ41 1=βρ4n =1.33×1051.14×7 =12.4meter.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?