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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
Source: WAEC / JAMB / NECO Classroom Archive (Record #68048)