# 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:

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

$\Rightarrow f_4 = 250 Hz$

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

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

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#### APPEARS IN

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