course Phy 122
Ch.11 (36,37,38,52,53,54)36. A fisherman notices that wave crests pass the bow of his anchored boat every 3.0s. He measures the distance between two crests to be 6.5m. How fast are the waves traveling?
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- v = λ/T v= 6.5m/3s = 2.17m/s
37. A sound wave in air has a frequency of 262Hz and travels with a speed of 343m/s. How far apart are the wave crests (compressions)?
- v= λf or λ=v/f 343m/s / 262Hz= 1.31m
38. a) AM radio signals have frequencies between 550kHz and 1600kHz and travel with a speed of 3.0x10^8m/s. What are the wavelengths of these signals? b) On FM, the frequencies range from 88MHz to 108MHz and travel at the same speed; what are their wavelengths?
-a) λ=v/f 3x10^8m/s / 550x10^3Hz = 545.45m
3x10^8m/s / 1600x10^3Hz = 187.5m
-b) λ=v/f 3x10^8m/s / 88x10^6Hz = 3.41m
3x10^8m/s / 108x10^6Hz = 2.78m
52. If a violin string vibrates at 440Hz as its fundamental frequency, what are the frequencies of the first four harmonics?
- fn=nf1 (fundamental frequency)
f1= 1(440Hz) = 440Hz
f2= 2(440Hz) = 880Hz
f3= 3(440Hz) = 1320Hz
f4= 4(440Hz) = 1760Hz
53. A violin string vibrates at 294Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (Only two-thirds of the string vibrates as a standing wave).
- 294Hz / (2/3) = 441Hz
54. A particular string resonates in four loops at a frequency of 280Hz. Name at least 3 other frequencies at which it will resonate.
-f4=280Hz fn=nf1 f1=fn/n f1=280Hz / 4 f1=70Hz
f2=2(70Hz) = 140Hz f3=3(70Hz) = 210Hz f5=5(70Hz) = 350Hz
very good work on these problems