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Radhika Batra Grade: 11
        The equation of a wave travelling on a string is 

Y = (0.10 mm) sin[(31.4 m-1)x + (314 s-1)t].
(a) In which direction does the wave travel? (b) Find the wave speed, the wavelength and the frequency of the wave. (c) What is the maximum displacement and the maximum speed of a portion of the string?
3 years ago

Answers : (1)

Navjyot Kalra
askIITians Faculty
654 Points
										Sol. The equation of the wave is given by

y = (0.1 mm) sin [(31.4 m–1)x +(314 s–1)t] y = r sin {(2πx / λ)} + ωt)
a) Negative x-direction
b) k = 31.4 m–1
⇒ 2 λ / λ = 31.4 ⇒ λ = 2π/31.4 = 0.2 mt = 20 cm
Again, ω = 314 s–1
⇒ 2πf = 314 ⇒ f = 314 / 2π = 314 / (2 * (3/14)} = 50 sec–1
∴ wave speed, v = λf = 20 * 50 = 1000 cm/s
c) Max. displacement = 0.10 mm
Max. velocity = aω = 0.1 * 10–1 * 314 = 3.14 cm/sec.
3 years ago
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