In-class problems 3 Solutions

# In-class problems 3 Solutions - with no amplitude...

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Name Student ID Section In-Class Problem, Week 4 22 April 2008 Show ALL your work, Total Points Possible = 7 1. A string with a mass of 6.02 g and a length of 7.14 m has one end attached to a wall; the other end is draped over a pulley and attached to a hanging object with a mass of 3.94 kg. If the string is plucked, what is the fundamental frequency of the vibration? (5 points) T = m o g = (3 . 94 kg )(9 . 81 m/s 2 ) = 38 . 65 N (+ 1pt) μ = m L = 0 . 00602 kg 7 . 14 m = 8 . 43 × 10 - 4 kg/m (+ 1pt) v = p T/μ = q 38 . 65 8 . 43 × 10 - 4 = 214 . 1 m/s (+ 1pt) λ = 2 L = 2(7 . 14 m ) = 14 . 28 m (+ 1pt) f = v/λ = 214 . 1 / 14 . 28 = 15 . 0 Hz (+ 1pt) 2. Explain how a musical instrument such as a piano may be tuned by using the phenomenon of beats. (2 points) A tuning fork or other type of pure–tone generator is needed that is at the desired frequency. You would then strike the tuning fork and pluck the corresponding string at the same time; if the piano string and tuning fork were exactly in tune, you would only hear one single pitch
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Unformatted text preview: with no amplitude modulation. If the two pitches were out of tune, you will hear beats. The piano string could then be tightened or loosened (to retune it) until the beat frequency between tuning fork and piano string goes to zero. (+1 pt for recognizing the need of tuning fork or something else that generates the pure–tone at the correct frequency, and for recogninzing that if they are in tune, there are no beats, if they are out of tune, you hear beats) (+1 pt for describing how to ﬁx the problem if they’re out of tune) Some possibly useful equations: y = y 1 + y 2 = A [sin( kx-ωt ) + sin( kx-ωt + φ )] = (2 A cos φ 2 ) sin( kx-ωt + φ 2 ) sin a + sin b = 2 cos( a-b 2 ) sin( a + b 2 ) Δ r = φ 2 π λ λ n = 2 L n ( n = 1 , 2 , 3 , ... ) f n = v λ n v = q T μ μ = m L 1...
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