A piano wire 50 cm long has a total mass of 10 g and its ...
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
Correct answer is A
T=800N; I=50cm=0.5m,
m=10g=0.01kg
fundamental freq: fo =?
fo = \frac{1}{21}√{T}{μ}
μ =\frac{m}{1}=\frac{0.01}{0.5}
⇒ f_o =\frac{1}{2×0.5}√\frac{800}{0.02}
f_o ⇒√ 40,000
⇒1st overtone = 2f_o =2×200 = 400Hz
⇒2nd overtone =3f_o =3×200=600Hz
∴3rd over tone= 4f_o =4×200=800Hz
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