Question

Calculate the frequency of the 3rd normal mode of a guitar string of length 40.0cm and mass 0.5g when stretched with a tension of 80N

Answer 1

frequency of 3rd normal mode of the guitar is 948.75 Hz

we have to calculate the frequency of the 3rd normal mode of a guitar string of length, l = 40 cm and mass, m = 0.5 g when stretched with a tension , T = 80N.

velocity of wave , v = √{T/μ}

here μ is mass per unit length and T is tension in stretched string.

so, μ = (0.5 × 10¯³kg)/(40 × 10¯² m) = 0.0005/0.4 = 0.00125 kg/m

Now, v = √{80/0.00125} = √{64000} ≈ 253 m/s

To find the frequency of 3rd mode, using formula

f = 3v/2L

= 3 × 253/2 × 0.40

= (759)/0.8

= 948.75 Hz