Wave motionHardBloom L3
Question
A transverse wave travelling on a taut string is represented by:
Y = 0.01sin2π(10t – x) → Y and x are in meter and 't' in second. Then,
Options
A.the speed of the wave is 10 m/s
B.closest points on the string which differ in phase by 60° are separated by (1/6) m
C.Maximum particle velocity is π/4 m/s
D.The phase of a certain point on the string changes by 120° in (1/20) seconds
Solution
Sol. y = 0.01 sin2π (10t – x)
vw = 10 m/s, k = 2π, ω = 20π
60° = $\frac{\pi}{3} = K\Delta x$
⇒ ∆x = $\frac{\pi}{3 \times 2\pi}$ = $\frac{1}{6}$m
vpmax = Aω = 0.01 × 20π = 0.2π = $\frac{\pi}{5}$m/s
120° = $\frac{2\pi}{3}$ = ω∆t
⇒∆t = $\frac{2\pi}{3 \times 20\pi} = \frac{1}{30}$ sec
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