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 . (ρsteel=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, = 7.8×10³ kg/m³

Volume of string can be calculated as:

V = πr²L = (3.14)(0.45×10^-3)²×2 = 1.27×10^-6 m³.

Mass of the string M= 7.8×10³×1.27×10^-6 = 9.9×10^-3 kg

Mass per unit length = πr² = 0.00495 kg/m

Wave speed along string V= √T/

Frequency of fundamental f₁ = 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