Harmonics of a Noon Hour Whistle in a Closed Air Column

In summary, the fundamental frequency produced by the noon hour whistle in the small town is equal to the speed of sound in air divided by four times the length of the whistle. The next harmonic is three times the fundamental frequency. To find the next harmonic, you would multiply the fundamental frequency by three.
  • #1
dance_sg
113
0

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?
 
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  • #2


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.
 
  • #3


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


dance_sg said:
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.
 
  • #5


so I am multiplying the wavelength by 4...
 
  • #6


dance_sg said:
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.
 
  • #7


so how do i solve for the wavelength then?
 
  • #8


dance_sg said:
so how do i solve for the wavelength then?
Wavelength = 4*length of the tube.
 
  • #9


0.750 x 4 then..
 
  • #10


dance_sg said:
0.750 x 4 then..
Use the relevant formula which you have mentioned, and find the frequency.
 
  • #11


ok. so that would be the frequency. in the question tho it says find the next harmonic. how do i do that?
 
  • #12


dance_sg said:
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.
 
  • #13


ok. so multiply what i got for the frequency by 3.
 
  • #14


dance_sg said:
ok. so multiply what i got for the frequency by 3.
Yes.
 
  • #15


thank you so much
 

Related to Harmonics of a Noon Hour Whistle in a Closed Air Column

1. What is the harmonics frequency problem?

The harmonics frequency problem is a phenomenon that occurs when a periodic signal contains multiple frequencies that are integer multiples of a fundamental frequency. This can result in unwanted distortions and interference in the signal.

2. How does the harmonics frequency problem affect electronic devices?

The presence of harmonics can cause electronic devices to malfunction or operate inefficiently. This can lead to increased power consumption, overheating, and potential damage to the device.

3. What causes the harmonics frequency problem?

The harmonics frequency problem can be caused by non-linear loads, such as electronic devices with power supplies, motors, and transformers. These loads can generate harmonics in the power system, which can then affect other devices connected to the same system.

4. How can the harmonics frequency problem be mitigated?

There are several ways to mitigate the harmonics frequency problem. One approach is to use harmonic filters, which are devices that reduce the level of harmonics in a signal. Another approach is to design and use power systems that can handle harmonic currents and voltages without causing interference.

5. Can the harmonics frequency problem be completely eliminated?

While it is not possible to completely eliminate harmonics, it can be minimized to a level that does not significantly affect electronic devices. This can be achieved through proper design and maintenance of power systems, as well as the use of harmonic filters and other mitigation techniques.

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