For what slide extensions will trombone produce max sound intensity?

[ppy]

Homework Statement

A 285Hz sound wave is directed into one end of a trombone slide A microphone is placed at the other end to record the intensity of sound waves that are transmitted through the tube. The straight sides of the slide are 80cm in length and 10cm apart with a semicircular bend at the end


For what slide extensions will the microphone detect a maximum of sound intensity?
express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas.

Homework Equations

maybe the equations for an open closed tube i think.

wavelength at specific mode= 4L/m
m=mode L= length

also V=frequency x wavelength

The Attempt at a Solution

L= 0.8m +0.05pi+ 0.8m (The 0.05pi is half the circumference to find the length of the semicircle)

Please i really want to understand this question but don't no where to go? Is a trombone an open closed tube?

 

[TSny]

Hello, ppy and welcome to PF!

Looks like you calculated the unextended length, L, of the trombone slide correctly

When the slide is "extended" it means that a certain extra length, x, is added to each of the straight sides. You need to find values of x that will produce maximum sound intensity at the microphone.

I think you want to treat the slide tube as open at both ends.

 

[ppy]

can i have a detailed solution

 

[Rob D]

As a very long time trombone player, I can say that I have never perceived any difference in heard volume from closed slide to fully extended using even airflow and at various harmonic levels. I think that you will find that the more excellent the quality of the instrument, the less difference there will be. I do not make trombones but I imagine that evenness across the slide positions would be something that they work to attain.

All I Know,
Rob

 

[TSny]

can i have a detailed solution

Our goal here is not to provide worked out solutions, but rather to help you get over the spots where you are stuck .

You've studied standing sound waves in a tube. Do you recall the condition that the length of the tube and the wavelength must satisfy in order to have a standing wave in a tube that is open at both ends?

 

[TSny]

As a very long time trombone player, I can say that I have never perceived any difference in heard volume from closed slide to fully extended using even airflow and at various harmonic levels. I think that you will find that the more excellent the quality of the instrument, the less difference there will be. I do not make trombones but I imagine that evenness across the slide positions would be something that they work to attain.

All I Know,
Rob

I've never played a trombone. I would guess, though, that as you extend the slide you also change the vibration frequency of your lips to maintain a resonant condition. I could be wrong.

Here we are assuming that we always put in the same frequency as we extend the slide. So, only certain positions of the slide would produce resonance. This is just an academic exercise that doesn't really correspond to playing the instrument.

 

[ppy]

hey thanks a lot guys i was able to complete the question and get the correct answer. :)