SPH3U: Module 8 Consolidation: Vibrations & Waves. Q&A

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Ally, Faatimah

Tuesday, June 7th, 2022

SPH3U: Module 8 Consolidation: Vibrations & Waves 1. A tuning fork produces a signal of 530 Hz. What frequency is: a. two octaves below this frequency?

530 =265 Hz 2 265 =132.5 Hz To go two octaves below: 2 To go one octave below:

Therefore, two octaves below the frequency of 530 Hz is: 530/22 = 132.5 Hz.

b. three octaves above this frequency?

To go one octave above: 530 ×2=1060 Hz To go two octaves above: 1060× 2=2120 Hz To go three octaves above: 2120 ×2=4240 Hz Therefore, three octaves above the frequency of 530 Hz is: 530 Hz.

× 23 = 4240

2. Certain pipe organs can act like air columns that are open at both ends. If the speed of sound is 343 m/s, how long must a pipe be to produce a frequency of 25 Hz (the lower hearing range of most adults)? ½ λ =l v = 343 m/s f = 25 Hz Wavelength:

v =f λ v λ= f 343 ¿ 25 ¿ 13.72m Length of the pipe: ½ (13.72) = l l = 6.86 m Therefore, the pipe must be 6.86 m long to produce a frequency of 25 Hz.

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Ally, Faatimah

Tuesday, June 7th, 2022

3. The "standard" note (A4 = 440 Hz) on a harp has a string length of 75 cm.

How long would the same string have to be to produce middle C (261.6 Hz)? l 1=75 cm→ 0.75 m f 1 =440 Hz l 2=? f 2=261.6 Hz Formula to solve for

l2 :

f 1 l1 = f 2 l2 440 0.75 = 261.6 l2 Solving for

l2 :

f l (¿ ¿1) (¿¿ 1) f2 ¿ l 2=¿ (440)(0.75) ¿ 261.6 330 ¿ 261.6 ¿ 1.26 m∨126 cm Therefore, the string would have to be 1.26 m/126 cm long in order to produce middle C.

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Ally, Faatimah

Tuesday, June 7th, 2022

4. An air column closed at one end, with a length of 25.3 cm, resonates in the first overtone. If the frequency of the sound wave is 1024 Hz, find the air temperature inside the column. l = 25.3 cm → 0.253 m f = 1024 Hz 1st overtone = 2nd harmonic → l = ¾ λ Wavelength: ¾ = 0.75

λ= ¿ 0.75 0.253 ¿ 0.75 ¿ 0.337 m Speed:

v =f λ ¿(1024)(0.337) ¿ 345.088 m/s Air Temperature: v = 332 + 0.59t 345.088 = 332 + 0.59t 345.088 - 332 = 0.59t 13.088 = 0.59t

(13.088) =t 0.59 22°C = t Therefore, the air temperature inside the column is 22°C.

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