- #1

chrisakatibs

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## Homework Statement

A 210 g bucket containing 12.5 kg of water is hanging from a steel guitar string with mass m = 8.58 g, density p = 7750 kg/m3, and diameter d = 1.00 mm. A) When the wind blows, it causes the cord to vibrate at what resonant frequency? B) Suddenly the bucket springs a leak in the bottom such that water drops out at a steady rate of 2.00 g/s. At what rate are the (i) wave speed, (ii) wavelength of the fundamental mode of vibration, and (iii) frequency changing? C) How long will it take until the vibration is no longer audible (between 20 Hz and 20,000 Hz)?

## Homework Equations

Many, wave equaitons, string tension etc.

## The Attempt at a Solution

First parts are here to confirm, need help with last part, I believe it should be just plugging 20 Hz into an equation.

V=sqrt(T*L/mass)

T=mg=(12.5 0.210)*9.81=124.6851 N

L=volume /area =(0.00858/7750)*10^(6)/(3.14*0.5^2)=1.41031436m

a)V=sqrt(124.6851*1.41031436/0.00858)=143.15997 m/s

frequency=velocity /2L=143.15997/(2*1.41031)=50.754 Hz

B)i) dv/dt= -0.0196*sqrt(L/(Tm))=0.01968*sqrt(1.41031436/(124.6851*0.00858))=0.0225960m/s^2

wave speed change rate = 0.01129 m /s^2

ii)wavelength of the fundamental mode of vibration change=1/(2*50.754*124.6851)=0.00007901056 m/s

iii)frequency changing=0.01129 /(2*1.4103143)=0.00400265387