Harmonics of a Noon Hour Whistle in a Closed Air Column

[dance_sg]

Homework Statement

A small town’s noon hour whistle is an air column 0.750 m long and closed at one end. Find the fundamental frequency and the next harmonic produced by this whistle when the speed of sound in air is 342 m/s.

Homework Equations

f= v/λ,

The Attempt at a Solution

would i first find the frequency, then divide that by 3 to get the 3rd harmonic? then take the same number i divided by 3, but divde it by two to find the second harmonic?

 

[rl.bhat]

In the closed pipe, length of the pipe for the fundamental frequency is equal to λ/4.
The next harmonics is three times the fundamental frequency.

 

[dance_sg]

so divide 0.750m by 4 to find the fundamental frequency? then how would i find the necxt harmoinic?

 

[rl.bhat]

so divide 0.750m by 4 to find the fundamental frequency? then how would i find the necxt harmoinic?

No.
λ = 4* length of the tube.

 

[dance_sg]

so I am multiplying the wavelength by 4...

 

[rl.bhat]

so I am multiplying the wavelength by 4...

No. In the problem the length of the tube is given, not the wavelength.
If you see the stranding wave in the tube closed at one end, you can see that length of then tube is equal to λ/4.

 

[dance_sg]

so how do i solve for the wavelength then?

 

[rl.bhat]

so how do i solve for the wavelength then?

Wavelength = 4*length of the tube.

 

[dance_sg]

0.750 x 4 then..

 

[rl.bhat]

0.750 x 4 then..

Use the relevant formula which you have mentioned, and find the frequency.

 

[dance_sg]

ok. so that would be the frequency. in the question tho it says find the next harmonic. how do i do that?

 

[rl.bhat]

ok. so that would be the frequency. in the question tho it says find the next harmonic. how do i do that?

Next frequency is equal to three times the fundamental frequency.

 

[dance_sg]

ok. so multiply what i got for the frequency by 3.

 

[rl.bhat]

ok. so multiply what i got for the frequency by 3.

Yes.

 

[dance_sg]

thank you so much