Question 118: Waves

Question

The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = $$-$$ 0.21 sin (x + 30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x $$	imes$$ 10$$-$$2 N. Value of x is _________. (Round off to the nearest integer)

Accepted Answer

$$\mu  = 0.135$$ gm/cm
$$\mu  = 0.135 	imes {{{{10}^{ - 3}}} \over {{{10}^{ - 2}}}}{{kg} \over m}$$
y = $$-$$0.21 sin (x + 30t)
$$v = {\omega  \over K} = {{30} \over 1}$$ = 30 m/s
v = $$\sqrt {{T \over \mu }} $$
T = v
2
$$	imes$$ $$\mu$$
T = (30)
2
$$	imes$$ 0.135 $$	imes$$ 10
$$-$$1
T = 900 $$	imes$$ 0.135 $$	imes$$ 10
$$-$$1
T = 12.15 N
T = 1215 $$	imes$$ 10
$$-$$2
N
x = 1215

Waves

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