Calculating Resonance Frequency of Original Metal Pipe

[ayrricjones]

Q: When a metal pipe is cut into two pieces, the lowest resonance frequency for one piece is 230 Hz and the other is 436 Hz.(a) what resonant frequency would have been produced by the original length of pipe?

From what I have so far:

1) the length of the two original pipes added together would give me the resonant frequency

2) the length of each pipe can be found by dividing the lamda for frequency for each pipe by two

3) Lamda can be found by the formula "v=(lamda)f," unfortunately I do not know the "v." What set of formula's or algebra can I use to find "v" ?

Thx ahead of time.

 

[quantumdude]

3) Lamda can be found by the formula "v=(lamda)f," unfortunately I do not know the "v." What set of formula's or algebra can I use to find "v" ?

It's the speed of sound, so you would just look it up.

 

[quicknote]

To calculate the resonant frequency of the original metal pipe, we need to use the formula v = λf, where v is the velocity of sound in the pipe, λ is the wavelength, and f is the frequency. We can rearrange this formula to solve for v by dividing both sides by λ, giving us v = f/λ. We also know that the lowest resonance frequency for one piece of the pipe is 230 Hz and for the other piece it is 436 Hz. From this, we can calculate the wavelength for each piece of the pipe by using the formula λ = v/f. Plugging in the values, we get λ1 = v/230 and λ2 = v/436.

Since the original pipe was cut into two pieces, we can assume that the total length of the two pieces is equal to the original length. This means that we can add the two wavelengths together to get the total wavelength for the original pipe, which is λ = λ1 + λ2 = v/230 + v/436.

Now, we can substitute this value for λ into the formula v = f/λ to solve for v. This gives us v = f/(v/230 + v/436). We can simplify this equation by multiplying both sides by (v/230 + v/436), giving us v^2 = f(v/230 + v/436). Finally, we can solve for v by taking the square root of both sides, giving us v = √(f(v/230 + v/436)).

Therefore, the resonant frequency of the original metal pipe would be √(f(v/230 + v/436)). We can plug in the values for either one of the pieces of the pipe to calculate the velocity of sound, and then use that value to calculate the resonant frequency of the original pipe.