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.
A.
800 Hz
B.
600 Hz
C.
400 Hz
D.
200 Hz
Correct answer is A
T=800N; I=50cm=0.5m,
m=10g=0.01kg
fundamental freq: \(f_o\) =?
\(f_o\) = \(\frac{1}{21}√{T}{μ}\)
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 = 2\(f_o\) =2×200 = 400Hz
⇒2nd overtone =3\(f_o\) =3×200=600Hz
∴3rd over tone= 4\(f_o\) =4×200=800Hz
