Question

A student uses a 2.00-m-long steel string with a diameter of
0.90 mm for a standing wave experiment. The tension on the string
is tweaked so that the second harmonic of this string vibrates at
22.0 Hz . (*ρ*steel=7.8⋅103 kg/m3)

Calculate the tension the string is under.

Calculate the first harmonic frequency for this sting.

If you wanted to increase the first harmonic frequency by 44 % , what would be the tension in the string?

Answer #1

Given: second harmonic frequency: 2f = 22Hz

i.e first harmonic frequency will be f = 11 Hz.

L = 2 m, d= 0.90 mm, =
7.8×10^{3} kg/m^{3}

Volume of string can be calculated as:

V = πr^{2}L = (3.14)(0.45×10^{-3})^{2}×2
= 1.27×10^{-6} m^{3}.

Mass of the string M= 7.8×10^{3}×1.27×10^{-6} =
9.9×10^{-3} kg

Mass per unit length =
πr^{2}
= 0.00495 kg/m

Wave speed along string V= √T/

Frequency of fundamental f_{1} = V/2L

√T/= 11×2×2

Hence Tension T = 9.58 N.

If you increase f by 44℅ you will get new frequency (f+0.44f)

Then put the same formula for tension

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