JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Waves & Sound

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 + 30 t)

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 \times 1 0^{- 2} N

. Value of x is ⋯⋯ . (Round-off to the nearest integer)

Answer: 1215

Solution

The phase of the wave gives

k = 1 m^{- 1}

and

ω = 30 s^{- 1}

, so the wave travels at

v = \frac{ω}{k} = 30 m/s

. The linear density is

μ = 0.135 g/cm = \frac{0.135 \times 1 0 ^{- 3} kg}{1 0 ^{- 2} m} = 1.35 \times 1 0^{- 2} kg/m

For a transverse wave on a stretched wire

v = \frac{T}{μ}

, so

T = μ v^{2} = 1.35 \times 1 0^{- 2} \times 900 = 12.15 N

Written in the form

x \times 1 0^{- 2}

N the tension is

1215 \times 1 0^{- 2}

N, so

x = 1215

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Integer answer