Question

A 121 cm-long, 3.8 g string oscillates in its m = 3 mode with a frequency of 144 Hz and a maximum amplitude of 5.0 mm. What are the wavelength and the tension in the string?

Answer 1

In the third mode

the length of the string L = 3*lambda/2

lambda = wavelength

wavelength = 2L/3 = 0.81 m <<<<======ANSWER

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harmonics of frequency = m*V/2L

given f = 144 for m = 3

144 = 3V/(2L)

V = 144*2*L/3

V = 144*2*1.21/3= 116.16 m/s

speed of wave in a string V = sqrt(T/u)

u = linear mass density = m/L

m = mass = 0.0038 kg

V = sqrt(TL/m)

116.16 = sqrt(T*1.21/0.0038)

tension T = 42.4 N   <<<<<<===========ANSWER