A transverse displacement of vibrating string is y = 0.06 sin ( 3 2 π ) x cos ( 120 π t ) . If the mass per unit length of a string is 4 × 1 0 − 2 kg / m , then the tension in the string will be

Question

A transverse displacement of vibrating string is y = 0.06 sin ( 3 2 π ​ ) x cos ( 120 π t ) . If the mass per unit length of a string is 4 × 1 0 − 2 kg / m , then the tension in the string will be

TestHub · Accepted Answer

The given equation of the standing wave is $y = 0.06 sin (\frac{2 π}{3} x) cos (120 π t)$ .

Comparing this with the standard equation $y = A sin (k x) cos (ω t)$ , we get:

$k = \frac{2 π}{3}$ and $ω = 120 π$

The wave speed $v$ is given by:

$v = \frac{ω}{k} = \frac{120 π}{\frac{2 π}{3}} = 180 m/s$

The velocity of a transverse wave on a stretched string is $v = \frac{T}{m}$ , where $T$ is the tension and $m$ is the mass per unit length.

Squaring both sides, we get $T = v^{2} m$ .

Substituting the given values $v = 180 m/s$ and $m = 4 \times 1 0^{- 2} kg/m$ :

$T = (180)^{2} \times 4 \times 1 0^{- 2}$

$T = 32400 \times 4 \times 1 0^{- 2} = 1296 N$

Answer: 1296 N

Physics - Wave on String Question with Solution | TestHub

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