First slide

Speed of wave

Question

Equation of transverse wave propagating in a string having linear mass density 10 gm/m is $y = 0.5 \sin (100 π t - 2.5 π x)$ , where x is m metre, y is in mm and t is in second. Then tension in the string is

Moderate

A

20 N
B

16 N
C

40 N
D

25 N

Solution

$Y = 0.5 \sin (100 π t - 2.5 π x)$
$∴ ω = 100 π r a d / s and K = 2.5 π m^{- 1}$
$∴$ Velocity of propagation, $V = \frac{ω}{K} = 40 m / s$
Now $\sqrt{\frac{T}{μ}} = V \Rightarrow T = (10 \times 10^{- 3}) \times {(40)}^{2} N = 16 N$

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