School

Fishers High School **We aren't endorsed by this school

Course

PHYSICS 101

Subject

Mechanical Engineering

Date

Dec 17, 2023

Pages

3

Uploaded by kraftluke11 on coursehero.com

The Science Of Acoustics
Homework 6
Name:
Please, show all your work clearly and and write down all your steps. Use proper units in all
your answers! Please be clear! I repeat on purpose.
Bottom line
: No Work, no credit. No
Kidding!
Problem 1 - Harmonics in pipes.
(30 Points)
Fill in the blanks in the table below. Please show all your work below the table, and sketch each
corresponding harmonic as well
Type of Pipe
Length of Pipe (m)
Name of Harmonic
Wavelength
λ
(m)
Frequency
f
(Hz)
Closed Pipe
0.45
Third Harmonic
Open Pipe
Second Harmonic
1.2
Closed Pipe
0.25
0.2
Open Pipe
Third Harmonic
0.4
Closed Pipe
First harmonic
3.6
Open Pipe
0.3
0.6

Problem 2 - More on standing waves in pipes.
(20 Points)
In this problem, assume that the speed of sound is
c
s
= 340 m/s. A long vertical tube of Length
H
is completely filled with water, and it has a small tap that can be used to drop the level of
water inside. A tuning fork of frequency 880 Hz is held ringing over the open end of the tube.
As water flows out of the tube, the air column inside grows longer. Calculate the first three air
column lengths,
L
1
,
L
2
and
L
3
for which resonance occurs (i.e. when the sound grows loud).
Draw three separate diagrams that show the standing waves in each case, and be sure to label
the locations of all the nodes and the antinodes.

Problem 3 - Fundamental of a Flute
(20 Points)
A flute is designed to play its fundamental note at 264 Hz, when the air temperature is 15
◦
C.
Calculate the length of the flute, and the frequencies of the second and third harmonics. Please
make sketches of all 3 harmonics.

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