First slide

Characterstics of wave

Question

A transverse wave described by equation y = 0.2 sin (x+30t) (where x and t are in metre and second) is travelling along a wire of cross-sectional area 1 mm² and density 8000 kg/m³. what is the tension in the string ?

Easy

A

20 N
B

7.2 N
C

30 N
D

14.4 N

Solution

The given equation is
$y = 0 \cdot 02 \sin 2 π [\frac{30 t}{2 π} + \frac{x}{2 π}] We have T = \frac{2 π}{30} or n = \frac{30}{2 π} and λ = 2 π V = nλ = \frac{30}{2 π} \times 2 π = 30 m / \sec Further v = \sqrt{(\frac{T}{m})} = 30 \frac{T}{m} = 900 or T = 900 \times 8000 \times (1 \times 10^{- 6}) = 7 \cdot 2 N$

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