Answer:
f₃ = 371.35 Hz
Step-by-step explanation:
First we need to find the speed o sound at given 24.2°C. For that purpose, we use the formula:
v = v₀√(T/T₀)
where,
v = speed of sound at 24.2° C = ?
v₀ = velocity of sound at 0° C = 331 m/s
T = Given Temperature = 24.2° C + 273 = 297.2 k
T₀ = Reference Temperature = 0° C + 273 = 273 k
Therefore,
v = (331 m/s)√(297.2 k/273 k)
v = 345.36 m/s
Now, for the third harmonic in the open air column:
λ₃ = (2/3) L
where,
λ₃ = wavelength = ?
L = Length of open air column = 1.4 m
Therefore,
λ₃ = (2/3)(1.4 m)
λ₃ = 0.93 m
So, for the frequency of the third harmonic, we use the formula:
v = f₃ λ₃
f₃ = v/λ₃
where,
f₃ = frequency of third harmonic = ?
v = speed of sound at that temperature = 345.36 m/s
λ₃ = wavelength of third harmonic = 0.93 m
Therefore,
f₃ = (345.36 m/s)/0.93 m
f₃ = 371.35 Hz