6 - Waves, Optics | Lecture Note

University:
High School
Course:
High School Physics
Academic year:

2024
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7
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6: Sound Waves AP FIZZ Motivation • If waves can be represented as sine/cosine functions, how do sound waves manifest in closed and open-ended tubes, how do they propagate in free space? Universal Wave Equation • All waves follow equation 𝑣 = 𝑓λ, where f = frequency, λ = wavelength, v = wave velocity. • True of sound waves in a medium, light waves in vacuum. Standing Waves (Resonant Lengths, Harmonics) • One open end: node at closed end, anti-node at open end, shortest tube contains ¼ λ, then ¾ λ, 5/4 λ, etc. • Two open ends: antinodes at both ends, shortest tube contains ½ λ, λ, 3/2 λ, etc. • Two closed ends: nodes at both ends, same as open ends. EX 1: A vibrating tuning fork is held near the mouth of a narrow plastic pipe partially submerged in water. The first loud sound is heard when the air column is 9.0cm long. The speed of sound is 342.8m/s in the room. Find a) λ of sound of tuning fork, b) length of air column for second and third resonances, and c) frequency of tuning fork. λ 𝐿1 = 4 λ = 4 9.0𝑐𝑚 = 36 𝑐𝑚, 𝑜𝑟 0.36𝑚 3λ 3(0.36) 𝐿2 = = = 0.27𝑚 4 4 5λ 5(0.36) 𝐿3 = = = 0.45𝑚 4 4 𝑣 = 𝑓λ 342.8 𝑓= = 952𝐻𝑧 0.36 Speed of Sound • Speed of sound depends on ambient temperature v = 331 + 0.59 𝑇 (T in °𝐶). • Use to find time or distance traveled by sound wave. EX 2: A large room is at 5.0°C. If the echo of a 256Hz sound pulse travels to a distant wall and returns in 0.350s, how far away is the wall and what is the wavelength of the sound? v = 331 + 0.59 5 = 333.95 𝑚/𝑠 𝑑 = 𝑣𝑡 𝑑 = 333.95 0.35 = 116.9 𝑚 116.9 𝑑𝑤𝑎𝑙𝑙 = = 58.4 𝑚 2 𝑣 = 𝑓λ 333.95 λ= = 1.30 𝑚 256