#4 in second image Trumpet PhysicsAs we learned in the video lesson, an open pipe of length L can create standingwaves at certain specific frequencies, given by:fn= n f12L= nfn = the frequency that creates a standing wave with n loops, in Hz= the "nth harmonic"fi = the frequency that creates a standing wave with 1 loop, in Hz= the "fundamental frequency"n = number of loops in the standing wavev = speed of the sound wave = 343 m/s (at 20° C)L= length of the pipe, in m%3DThe fundamental frequency, f1, is the lowest frequency that makes a standing wave onthe pipe. The higher frequencies or “harmonics" are multiples of the fundamental: f2is twice as much as f1; f3 is three times as big as f1, and so on.A trumpet is essentially a long, curved open pipe. (Actually, its geometry ismore complicated, but it is designed to produce the same set of frequencies that anopen pipe would. So close enough.) It has three valves, each of which is connected toan extra bit of tubing.When no valves are pushed, the sound wave passes straight through the horn,travelling a distance L. When a valve is pushed, it opens up the extra bit of tubing,which increases the length L of the horn slightly. According to the equation above,increasing the length L lowers the frequency of the standing wave, which produces alower tone or note. So, when a valve is pushed, it lowers the note the horn produces.Pushing a valve with a longer tube lowers the note even more. Opening more than onevalve makes the sound travel through more than one extra bit of tubing, lowering thenote even further. By picking the right combination of valves, the trumpet can makeany note on the musical scale.Directions: Here are some practice problems to make you familiar with theseconcepts. Please review the following. Assume the speed of sound is 343 m/s. 1. When no valves are pushed, the sixth harmonic of the horn (n = 6) produces afrequency of f6 = 698 Hz (an F). Use that information, and rearrange theequation above to calculate the length L of the trumpet's pipe when no valvesare used.2. When the first valve is pushed, the frequency of the sixth harmonic changes tofo = 622 Hz (an E-flat). Calculate the new length of the pipe L.3. The new length is slightly longer than the original length, because of the addedlength of the tubing attached to the first valve. Subtract the two lengths to findthe length of the tube attached to the first valve.4. When the second valve (only) is pushed, the frequency of the 6™ harmonic changesto fo = 659 Hz (an E). What is the new length of the pipe L?5. The difference in length between Step 4 and Step 1 is due to the length of the tubingattached to the second valve. Calculate the length of the tube attached to thesecond valve.6. When the third valve (only) is pushed, the frequency of the 6th harmonic changes tofo = 585 Hz (a D). What is the new length of the pipe L?7. The difference in length between Step 6 and Step 1 is due to the length of the tubingattached to the third valve. Calculate the length of the tube attached to the thirdvalve.8. The trumpet player now pushes both the 1" and 2nd valves, opening both bits ofextra tubing. What is the new length L of the horn?9. What is the frequency of the 6th harmonic produced in Problem 8?10. The trumpet player now pushes both the 1st and 3ª valves, opening both bits ofextra tubing. What is the new length L of the horn? What is the frequency ofthe 6th harmonic produced?11. The trumpet player now pushes both the 2nd and 3d valves, opening both bits ofextra tubing. What is the new length L of the horn? What is the frequency ofthe 6th harmonic produced?

Answered: Image /qna-images/answer/a5fa29b6-a49a-4a44-9cfe-d44cac6191ea.jpg

Answered: 4. When the second valve (only) is…

4. When the second valve (only) is pushed, the frequency of the 6™ harmonic changes to fo = 659 Hz (an E). What is the new length of the pipe L?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Properties of sound

A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).

Quality Of Sound

A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.

Categories of Sound Wave

People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.

Question

#4 in second image

Trumpet Physics
As we learned in the video lesson, an open pipe of length L can create standing
waves at certain specific frequencies, given by:
fn
= n f1
2L
= n
fn = the frequency that creates a standing wave with n loops, in Hz
= the "nth harmonic"
fi = the frequency that creates a standing wave with 1 loop, in Hz
= the "fundamental frequency"
n = number of loops in the standing wave
v = speed of the sound wave = 343 m/s (at 20° C)
L= length of the pipe, in m
%3D
The fundamental frequency, f1, is the lowest frequency that makes a standing wave on
the pipe. The higher frequencies or “harmonics" are multiples of the fundamental: f2
is twice as much as f1; f3 is three times as big as f1, and so on.
A trumpet is essentially a long, curved open pipe. (Actually, its geometry is
more complicated, but it is designed to produce the same set of frequencies that an
open pipe would. So close enough.) It has three valves, each of which is connected to
an extra bit of tubing.
When no valves are pushed, the sound wave passes straight through the horn,
travelling a distance L. When a valve is pushed, it opens up the extra bit of tubing,
which increases the length L of the horn slightly. According to the equation above,
increasing the length L lowers the frequency of the standing wave, which produces a
lower tone or note. So, when a valve is pushed, it lowers the note the horn produces.
Pushing a valve with a longer tube lowers the note even more. Opening more than one
valve makes the sound travel through more than one extra bit of tubing, lowering the
note even further. By picking the right combination of valves, the trumpet can make
any note on the musical scale.
Directions: Here are some practice problems to make you familiar with these
concepts. Please review the following. Assume the speed of sound is 343 m/s.

1. When no valves are pushed, the sixth harmonic of the horn (n = 6) produces a
frequency of f6 = 698 Hz (an F). Use that information, and rearrange the
equation above to calculate the length L of the trumpet's pipe when no valves
are used.
2. When the first valve is pushed, the frequency of the sixth harmonic changes to
fo = 622 Hz (an E-flat). Calculate the new length of the pipe L.
3. The new length is slightly longer than the original length, because of the added
length of the tubing attached to the first valve. Subtract the two lengths to find
the length of the tube attached to the first valve.
4. When the second valve (only) is pushed, the frequency of the 6™ harmonic changes
to fo = 659 Hz (an E). What is the new length of the pipe L?
5. The difference in length between Step 4 and Step 1 is due to the length of the tubing
attached to the second valve. Calculate the length of the tube attached to the
second valve.
6. When the third valve (only) is pushed, the frequency of the 6th harmonic changes to
fo = 585 Hz (a D). What is the new length of the pipe L?
7. The difference in length between Step 6 and Step 1 is due to the length of the tubing
attached to the third valve. Calculate the length of the tube attached to the third
valve.
8. The trumpet player now pushes both the 1" and 2nd valves, opening both bits of
extra tubing. What is the new length L of the horn?
9. What is the frequency of the 6th harmonic produced in Problem 8?
10. The trumpet player now pushes both the 1st and 3ª valves, opening both bits of
extra tubing. What is the new length L of the horn? What is the frequency of
the 6th harmonic produced?
11. The trumpet player now pushes both the 2nd and 3d valves, opening both bits of
extra tubing. What is the new length L of the horn? What is the frequency of
the 6th harmonic produced?

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