A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20° C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s . Does the fundamental frequency increase or decrease? By how much?

Question

A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20° C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s . Does the fundamental frequency increase or decrease? By how much?

Accepted Answer

Hey, everyone. So this problem is dealing with sound waves in a pipe where we have one open end and one closed end. Let's see what it us. Two students are examining the properties of sound using a cylindrical residence chamber that is modeled as a 200 centimeter long open closed tube. The experiment begins with the chamber's air temperature at degrees Celsius. As the students introduce heat to the chamber, the air temperature inside the tube rises causing the speed of sound to reach 361 m per second, determine if the fundamental frequency of the residence chamber increases or decreases. And by what amount take the speed of sound and air at 27 degrees Celsius to be 330 m per second. Our multiple choice answers here are a increases by 3.88 Hertz B decreases by 3.87 Hertz C increases by 2.35 Hertz or D decreases by 2.35 Hertz. So the first thing we can do is recall that our frequency in an open close tube situation is given by F equals N V divided by four L where N is your number of harmonics fundamental frequency means that N equals one, that's the definition of fundamental frequency. And so we can find what our frequency is initially before they introduce this heat. And then we can find the frequency after they introduce the heat. And from there, we'll know if it increased or decreased. So our initial frequency was um we, what we know that our initial frequency, excuse me, we are selling for our initial frequency N is one multiplied by speed which was given to us 330 m per second, divided by four, multiplied by the length 200 centimeters. We're gonna rewrite that as two m and that equals 400 or sorry, 41.25 Hertz, 41.25 Hertz. Our final frequency after the heat is added, we know the speed increased to 361 m per second. Our length is still the same two m. And so that gives us 45. Hertz. We can see when we look at F F minus F I that our final frequency is higher and it is higher by 3.88 Z. And so that is the answer when we look at our multiple choice answers that aligns with answer choice A it increases by 3.88 Hertz. So that's all we have for this one. We'll see you in the next video.

A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20° C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s . Does the fundamental frequency increase or decrease? By how much?

Verified Solution

Key Concepts

Fundamental Frequency

Speed of Sound

Effect of Temperature on Sound