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...

Assessment: JAMB UTME - Physics - 2023 Subject: Physics

Question 1 Report

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

Answer Details

T=800N; I=50cm=0.5m,

m=10g=0.01kg

fundamental freq: $f_{o}$ =?

$f_{o}$ = $\frac{1}{21} \sqrt T μ$

μ = $\frac{m}{1}$ = $\frac{0.01}{0.5}$

⇒ $f_{o}$ = $\frac{1}{2 \times 0.5}$ √ $\frac{800}{0.02}$

$f_{o}$ ⇒√ 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

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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...

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