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JAMB Physics 2023 Paper
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© africaexams.com
Question : 34
Total: 65
A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the frequency of the wire when it sounds its third overtone note.
800 Hz
600 Hz
400 Hz
200 Hz
Validate
Solution:
T=800N; I=50cm=0.5m,
m=10g=0.01kg
fundamental freq:
f
o
f_o
f
o
=?
f
o
f_o
f
o
=
1
21
T
μ
\frac{1}{21}\sqrt{T}\mu
21
1
T
μ
μ =
m
1
\frac{m}{1}
1
m
=
0.01
0.5
\frac{0.01}{0.5}
0.5
0.01
⇒
f
o
f_o
f
o
=
1
2
×
0.5
\frac{1}{2 \times 0.5}
2
×
0.5
1
√
800
0.02
\frac{800}{0.02}
0.02
800
f
o
f_o
f
o
⇒√ 40,000
⇒1st overtone = 2
f
o
f_o
f
o
=2×200 = 400Hz
⇒2nd overtone =3
f
o
f_o
f
o
=3×200=600Hz
∴3rd over tone= 4
f
o
f_o
f
o
=4×200=800Hz
© africaexams.com
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