Part A Constants When it is vibrating in its second overtone, find the frequency

Question

Part A Constants When it is vibrating in its second overtone, find the frequency at which it is vibrating. A 85.0 cm wire of mass 6.60 g is ted at both onds and adjusted to a tension of 45.0 N You may want to review (Pages 373-374) For related problem-sclving tips and strategies, you may want to viow a Video Tutor Solution of Abass sting fa Hz Submit PartE When it is vibrating in its second overtone, find the wavelength at which it is vibrating As- Submit Part When it is vibrating in its second overtone, find the frequency of the sound waves it is praducing. Submit Request Answer

Explanation / Answer

Given

length of the wire is L = 0.85 m , mass m = 6.60*10^-3 kg

tension is T = 45.0 N

we know that the speed of the wave on string is

v = sqrt(T/mue)

mue is linear mass density mue = m/L = 6.60*10^-3/0.85 = 0.00776471 kg/m

v = sqrt(45/0.00776471) m/s

v = 76.13 m/s

the harmonics of the string tied at both ends are

f1 = v/2L ---->first harmonic

f2 = 2v/2L = 2f1 ----> second harmonic and first overtone

f3 = 3V/2l = 3f1 ----> third harmonic and second overtone

Part A

the frequency is f3 = 3*f1 = 3*(76.13/(2*0.85)) Hz = 134.3471 Hz

Part B

from the relation v = Lambda*f

for second overtone v = Lambda*f3

lambda = v/f3 = 76.13/134.3471 m = 0.5666 m

Part C

frequency of the sound wave is same as the frequeny in the part A = 134.3471 Hz

Part D

the wavelength is V = lambda*f3

where V is the speed of the sound in air = 343 m/s

lambda = 343/134.3471m = 2.5531 m

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