Melodious Guitar Problem

Classical Mechanics Level 2

A guitar string is 1.2 m long and has a tension of 400 N . The mass of the string is 0.480 g .

Calculate

  • the mass per unit length of the string
  • the speed of waves on it.
3.2 ∗ 1 0 − 3 3.2*10^{-3} kg/m, 1000 m/s 5 ∗ 1 0 − 4 5*10^{-4} kg/m, 400 m/s 8 ∗ 1 0 − 5 8*10^{-5} kg/m, 200 m/s 4 ∗ 1 0 − 4 4*10^{-4} kg/m, 1000 m/s

Nabhanshul Satra by Nabhanshul Satra , 24, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Arsalan Iqbal
Apr 19, 2014

To find mass per unit length, we first convert mass from gram to Kg. i.e: 0.480/1000 = 4.8e-4 Kg. Now, finding mass per unit length = 4.8e-4/1.2 = 4e-4 Kg/m. Secondly, to find the speed of waves, using formula: Sq.root(Tension/Mass per unit length) = Sq root(400/4e-4) = 1000m/s. ~Answer~

12 Helpful 0 Interesting 0 Brilliant 0 Confused
Bernardo Sulzbach
Jun 23, 2014

m L = 4.8 ⋅ 1 0 − 4 kg 1.2 m = 4.0 ⋅ 1 0 − 4 kg m − 1 \frac{m}{L}=\frac{4.8\cdot{}10^{-4} \text{ kg}}{1.2 \text{ m}}=4.0\cdot{}10^{-4} \text{ kg} \text{ m}^{-1}

v = F ( m L ) = ( 400 N ) ( 1.2 m ) 4.8 ⋅ 1 0 − 4 kg = 1 ⋅ 1 0 6 m 2 s − 2 = 1 0 3 m s − 1 v=\sqrt{\frac{F}{\left(\frac{m}{L}\right)}}=\sqrt{\frac{\left(400 \text{ N}\right) \left(1.2 \text{ m}\right)}{4.8\cdot{}10^{-4} \text{ kg}}}=\sqrt{1\cdot{}10^{6} \text{ m}^2 \text{ s}^{-2}}=10^3 \text{ m s}^{-1}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...