A string on a one stringed instrument is 75.cm long and has a mass of 5.00g and

Question

A string on a one stringed instrument is 75.cm long and has a mass of 5.00g and is tightened to a tension of 540N. a) What is the speed of the wave on the string? b) What are the wavelength and frequency of the fundamental on the string? c) What is the wavelength of the sound wave produced by this vibration? d) What are the frequencies of the next two higher harmonics of this instrument? In the junk yard band, Bill plays the pipes...that is, he bangs on pipes with a mallet. One pipe is 0.84m long and open on both ends. a) What are the fundamental and first two overtones of this pipe? b) Russel stuffs a tennis ball in one end, effectively closing off that end. What are the fundamental and next two higher harmonics of the pipe now? Mrs. A drives a blue sedan to the right at a steady 40m/s. A pig named Max sits in the back seat squealing "wheee" all the way home. Max squeals at a frequency of 1200 Hz. a) Max's friend Josh warts patiently for Max to arrive home. What frequency squeal does Josh hear? b) Max's friend Lucy runs to meet him. She is traveling towards the car at a steady 30m/s. What frequency squeal does Lucy hear? c) Max's sister Karen runs away as the sedan approaches. Karen is traveling at 20m/s away from the sedan. What frequency squeal does Karen hear? Wendy is being chased by a bee named Peter! The bee buzzes at f = 1450Hz. Wendy, traveling at 32m/s, hears 1520Hz. What is the bee's speed? Is it catching up to Wendy?

Explanation / Answer

H1

a) v (speed of wave) = sqroot ( T/ m/L)= sqroot ( 540 x 75 x 10^-2/ 5 x 10^-3) = sqroot ( 540x 75 x 10 /5) = 284. 6 m/s

b) fundamental freqiuency =284. 6 / 2(L) = 189.736 hz, fundamental wavelength= 284. 6 / 189.736= 1.5 m apprx

c) wavelength= 344/ 189.736 = 1.813 m apprx

d) f2= 2 ( 189.736 ) = 379.472 hzm, f3= 3(189.736 )= 569.208 hz

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