f3 11 Hz (b) How many harmonic frequencies of this pipe lie in the audible range, from 20 Hz to 20000 Hz? 280 (c) What are the three lowest possible frequencies if the pipe is closed at on end and open at the other? f₁ = f3 = f5 = Hz Hz Hz
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.
![SOLUTION
(A) Find the frequencies if the pipe is open at both ends.
Substitute into whole harmonics
equation, with n = 1.
Multiply to find the second and third
harmonics.
This works out to n = 286.88, which
= 287
must be truncated down (n
gives a frequency over 2.00 x 104 Hz).
The next two harmonics are odd
multiples of the first:
V
2L
f₂ = 2f₁ = 139 Hz
f₁
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(B) How many harmonics lie between 20 Hz and 20000 Hz for this pipe?
Set the frequency in the harmonics
equation equal to 2.00 x 104 Hz and
solve for n.
343 m/s
2. (2.46 m)
fn
=
=
f₁
V
(C) Find the frequencies for the pipe closed at one end.
Apply the one end open harmonics
equation with n = 1.
2L
n = 286
343 m/s
2(2.46 m)
=
= n
V
4L
f3 = 3f₁ = 105 Hz
343 m/s
4(2.46 m)
= 69.7 Hz
f3 = 3f₁ =
=
= 209 Hz
=
2.00 × 104 Hz
34.9 Hz
f5 = 5f₁ = 175 Hz](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5630fc0f-1d39-4405-9289-17dd8428ca98%2F7b5211f1-fc1c-4e16-82e6-77c4402a6bc5%2F53bqahe_processed.png&w=3840&q=75)
![f3
=
Hz
(b) How many harmonic frequencies of this pipe lie in the audible range, from 20 Hz to 20000 Hz?
280
(c) What are the three lowest possible frequencies if the pipe is closed at on end and open at the
other?
f₁ =
f3
f5 =
=
Hz
Hz
Hz](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5630fc0f-1d39-4405-9289-17dd8428ca98%2F7b5211f1-fc1c-4e16-82e6-77c4402a6bc5%2F3hmnni_processed.png&w=3840&q=75)
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