What is the relationship between the width of an open organ pipe and its pitch?

[zorro]

Homework Statement

Given two statements:

Statement 1: Narrower the open organ
pipe, higher will be the
pitch.
Statement 2: The frequency of open
organ pipe depends on its
radius.

(1) Both statements statement 1 and
statement 2 are true and statement 2
is reason for statement 1

(2) Both statement 1 and statement 2
are true but statement 2 is not
reason for statement 1

(3) Statement 1 is true but statement 2
is false

(4) Statement 1 is false but statement 2
is true

The Attempt at a Solution

I believe the answer is (3) because the expression for frequency of the sound through an organ pipe depends on velocity and wavelength which do not depend on radius of the pipe. But this is wrong.

 

[tiny-tim]

Statement 1: Narrower the open organ
pipe, higher will be the
pitch.
Statement 2: The frequency of open
organ pipe depends on its
radius.
…
I believe the answer is (3) because the expression for frequency of the sound through an organ pipe depends on velocity and wavelength which do not depend on radius of the pipe. But this is wrong.

"narrower" means thinner, so smaller radius

 

[zorro]

Hi tiny-tim!

I'm afraid you did not get my question right.

I believe the answer is (3) because the expression for frequency of the sound through an organ pipe depends on velocity and wavelength which do not depend on radius of the pipe

 

[Dadface]

Abdul,look up "end correction"

 

[tiny-tim]

I'm afraid you did not get my question right.

But your own reasoning shows that statement (1) cannot be true.

(and I'm pretty sure you're intended to ignore the open end correction)

 

[zorro]

Abdul,look up "end correction"

Yeah I know about it but can 'end correction' be the sole reason for its dependency on radius?

But your own reasoning shows that statement (1) cannot be true.

I did not notice that
If we ignore the end correction then based on what mathematical relationship can we deduce the correct answer given [(1)]?

 

[Dadface]

The question didn't state that the frequency is solely dependent on radius but the implication is there.A badly written question.

 

[tiny-tim]

Statement 1: Narrower the open organ
pipe, higher will be the
pitch.
Statement 2: The frequency of open
organ pipe depends on its
radius.

(1) Both statements statement 1 and
statement 2 are true and statement 2
is reason for statement 1

If we ignore the end correction then based on what mathematical relationship can we deduce the correct answer given [(1)]?

I thought you said Statement 2 was false?

 

[zorro]

I thought you said Statement 2 was false?

Yes you are right, I thought that statement 2 is false (so option 3 according to me). But the correct answer given is option (1), and I asked you with what mathematical relationship can we deduce it?

 

[Dadface]

You don't need mathematical relationships,just look at it and if necessary sketch it.If the pipe is narrower then the effective length of the pipe(actual length plus added length due to end corrections)is shorter.This results in shorter wavelengths and higher frequencies.