Answer:
f = 459.8 Hz
Explanation:
When a trumpet is playing it is an open tube at both ends, therefore there is a belly in each one, the resonance occurs to
λ = 2L 1st harmonic
λ = 2L /2 2nd harmonic
λ = 2L /3 3rd harmonic
the speed of the wave is
v = λ f
λ = v / f
we substitute in the third harmonic
[tex]\frac{v}{f} = \frac{2L}{3}[/tex] (1)
L = [tex]\frac{3}{2} \ \frac{v}{f}[/tex]
L = [tex]\frac{3}{2} \ \frac{343}{ 510}[/tex]
L = 1.009 m
indicates that to add ΔL = 0.110 m, so the total length is
L_total = L + ΔL
L _total = 1.009 + 0.110
L _total = 1,119 m
we use equation 1
f = [tex]\frac{3}{2} \ \frac{v}{L_{total}}[/tex]
f = [tex]\frac{3}{2} \ \frac{343}{1.119}[/tex]
f = 459.8 Hz
