First slide

Equation of wave

Question

The linear density of a vibrating string is $10^{- 4}$ kg/m. A transverse wave is propagating on the string, which is described by the equation y = 0.02 sin (x + 30 t), where x and y are in metres and time t in seconds. Then tension in the string is

Easy

A

0.09 N
B

0.36 N
C

0.9 N
D

3.6 N

Solution

y = 0.02 sin (x + 30t), Comparing with standard equation y = A sin(Kx + wt), w = 30, K = 1
Velocity of wave, $v = \frac{ω}{K} = \frac{30}{1} = 30 m / s$
$v = \sqrt{\frac{T}{m}} g i v e s$ Tension T = $v^{2}$ m = (30 $)^{2}$ × $10^{- 4}$
= 0.09 N

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