A trumpet plays its 3rd harmonic at 510 Hz. It then opens a valve, which adds 0.110 m to its length. What is the new 3rd harmonic frequency? (Hint: Find the original length.) (Speed of sound = 343 m/s) (Unit = Hz)​

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

                       (1)

            L =

            L =

            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 =  

            f =

            f = 459.8 Hz

well, you would divide 135 by 33 to get your answer. then that is how many seconds it would take. boardman should fly about 132 m or 4.090909090909091 seconds.