A Steel Wire of Mass 4⋅0 G and Length 80 Cm is Fixed at the Two Ends. the Tension in the Wire is 50 N. Find the Frequency and Wavelength of the Fourth Harmonic of the Fundamental. - Physics

Sum

A steel wire of mass 4⋅0 g and length 80 cm is fixed at the two ends. The tension in the wire is 50 N. Find the frequency and wavelength of the fourth harmonic of the fundamental.

Solution

Given:
Mass of the steel wire = 4.0 g
Length of the steel wire = 80 cm = 0.80 m
Tension in the wire = 50 N
Linear mass density (m)

$= \left( \frac{4}{80} \right) g/cm = 0 . 005 kg/m$

$\text{ Wave speed, } \nu = \sqrt{\left( \frac{T}{m} \right)}$

$= \sqrt{\left( \frac{50}{0 . 005} \right)} = 100 m/s$

$\text{ Fundamental frequency ,} f_o = \frac{1}{2L}\sqrt{\left( \frac{T}{m} \right)}$

$= \frac{1}{2 \times 0 . 8} \times \sqrt{\left( \frac{50}{0 . 005} \right)}$

$= \frac{100}{2 \times 0 . 8} = 62 . 5 Hz$

$\text { First harmonic = 62 . 5 Hz }$

If   f_4  =frequency  of  the  fourth  harmonic:

$\Rightarrow f_4 = 4 f_0 = 62 . 5 \times 4$

$\Rightarrow f_4 = 250 Hz$

$\text{ Wavelength of thefourth harmonic,} \lambda_4 = \frac{\nu}{f_4} = \frac{100}{250}$

$\Rightarrow \lambda_4 = 0 . 4 m = 40 cm$

Is there an error in this question or solution?

APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 15 Wave Motion and Waves on a String
Q 36 | Page 326