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Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWaves5 Marks
Question
The transverse displacement of a string (clamped at its both ends) is given by
$\text{y}(\text{x, t})=0.06\sin\Big(\frac{2\pi}{3}\text{x}\Big)\cos(120\pi\text{ t})$
where x and y are in m and t in s. The length of the string is $1.5m$ and its mass is $3.0 \times 10^{–2}kg$.
Answer the following:
Determine the tension in the string.
✓

Answer

The velocity of a transverse wave travelling in a string is given by the relation:
$\text{v}=\sqrt{\frac{\text{T}}{\mu}}\ \dots(\text{i})$
Where,
Velocity of the transverse wave, v = 180m/ s
Mass of the string, $m = 3.0 \times 10^{-2}kg$
Length of the string, l = 1.5m
Mass per unit length of the string, $\mu=\frac{\text{m}}{\text{l}}$
$=\frac{3.0}{1.5}\times10^{-2}$
$=2\times10^{-2}\text{kg m}^{-1}$
Tension in the string = T
From equation (i), tension can be obtained as:
$\text{T}=\text{v}^2\mu$
$=(180)^2\times2\times10^{-2}$
$=648\text{N}$

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