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PART - 2 CH - 14 Waves — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 14 Waves4 Marks
Question
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is $3.5 \times 10^{-2}$ kg and its linear mass density is $4.0 \times 10^{-2} kg m ^{-1}$. What is (a) the speed of a transverse wave on the string and (b) the tension in the string?
✓

Answer

Given :
Frequency $n =45$
Mass of wire $( M )=3.5 \times 10^{-2} kg$
$m=$ Unit length mass $=$ Linear mass density $=4.0 \times 10^{-2} kg / m$
Let if length of wire is $l$ then
$\text { Formula }l =\frac{M}{m}=\frac{3.5 \times 10^{-2}}{4 \times 10^{-2}} $
$=0.875 m$
(a) Speed of transverse wave in wire $v =$ ?
(b) Tension in wire $T =$ ?
(a) Frequency of basic mode in oscillation
$n=\frac{v}{\lambda}=\frac{v}{2 l}$
$\because$ Basic mode in oscillation
$L=\frac{\lambda}{2}$
or $\quad\lambda=2 l$
$\therefore \quad v =n \times 2 l$
Put the value
$v =45 \times 2 \times 0.875 $
$=78.75 m / s $
$\simeq 79 m / s$
(b) We can find tension in wire
$v=\sqrt{\frac{T}{m}}$
or $\quad T=v^2 \times m$
Put the value
$T =(78.75)^2 \times 4 \times 10^{-2} $
$=248.06 N$

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