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

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.