A 280 Hz sound wave is directed into one end of the trombone slide seen below. A

Question

A 280 Hz sound wave is directed into one end of the trombone slide seen below. A microphone is polaced at the other end to record the intensity of sound waves that are transmitted through the tube. The straight sides of the slide are 80 cm in length and 10 cm apart with a semicircular bend at the end. For what slide extensions s will the microphone detect a maximum of sound intensity? The answer is 4 cm, 35cm, 65 cm. I did 1.6m+ pi(5)+2s = m(lambda) lambda = v/f = 343/280 Then I solved for s by trying out different values of m but this is WRONG. What did I do wrong? How can I solve this?

Explanation / Answer

first find an equation for the total length of the entire pathway (tube) [let it be L] L= the two straight parts + the semicircular part + the extendable part (s) = 2(0.8m) + 2pi(0.05m)/2 + 2s = 1.6 + 0.05pi + 2s (meters) then use the equation lambda = 2L/m (where lambda = v/f =343/280 = 1.225 m; and m = number of modes) substitute the L above into this equation. so you will have: 1.225 = 2[1.6 + 0.05 pi + 2 s ]/m ...then u just have to plug in m = 1, 2, 3, 4....BUT if u plug in 1 and 2, you will have a negative number which means the total length of the tube is larger than your wavelength lambda so u cannot have the fundamental or secondary harmony in this case..therefore you will have to use the following m = 3, 4, and 5 to get ur answers. Then it's just simple algebra and u should end up with s=0.04 m, 0.35 m n 0.65 m respectively.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.