The equation of a wave on a string of linear mass density $0.04 \mathrm{~kg} \mathrm{~m}^{-1}$ is given by $y=0.02(m) \sin \left[2 \pi\left(\frac{t}{0.04(s)}-\frac{x}{0.50(m)}\right)\right]$. The tension in the string is

JEE Main · 2010 · 11 Apr 2010 · Offline · Waves & Sound

The equation of a wave on a string of linear mass density

0.04 kg m^{- 1}

is given by

y = 0.02 (m) sin [2 π (\frac{t}{0.04 ( s )} - \frac{x}{0.50 ( m )})]

. The tension in the string is

Answer: (D)

Comparing the given wave

y = 0.02 sin [2 π (\frac{t}{0.04} - \frac{x}{0.50})]

with the standard form

y = A sin (ω t - k x)

, we read off

ω = \frac{2 π}{0.04} = 50 π

rad/s and

k = \frac{2 π}{0.50} = 4 π

rad/m. The wave speed is

v = ω / k = 50 π /4 π = 12.5

m/s. On a string the speed is fixed by the tension and the linear mass density through

v = T / μ

, so

T = μ v^{2} = 0.04 \times (12.5)^{2} = 6.25

JEE Main · 2010 · 11 Apr 2010 · Offline · Single correct option