A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the

Explanation

Step 1: Identify given values and what to find
Given: L = 50 cm = 0.5 m, m = 10 g = 0.01 kg, T = 800 N
Find: Frequency of third overtone (4th harmonic)

Step 2: Calculate linear mass density
Formula: μ = m/L
μ = 0.01/0.5 = 0.02 kg/m

Step 3: Calculate wave velocity in wire
Formula: v = √(T/μ)
v = √(800/0.02) = √40000 = 200 m/s

Step 4: Calculate fundamental frequency
Formula: f₀ = v/(2L)
f₀ = 200/(2 × 0.5) = 200 Hz

Step 5: Calculate third overtone frequency
Third overtone = 4th harmonic = 4f₀
f = 4 × 200 = 800 Hz

Step 6: The answer is 800 Hz