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A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x-axis with a speed of 128 m/s and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is
A
y = (0.02) m sin (7.85x – 1005t)
B
y = (0.02) m sin (7.85x + 1005t)
C
y = (0.02) m sin (15.7x – 2010t)
D
y = (0.02) m sin (15.7x + 2010t)
Detailed Solution
Amplitude: A = 2 cm = 0.02 m
5 complete waves fit in 4 m, so $\lambda = \frac{4}{5} = 0.8$ m
Wave number: $k = \frac{2\pi}{\lambda} = \frac{2\times3.14}{0.8} = 7.85$ rad/m
Angular frequency: $\omega = vk = 128\times7.85 = 1005$ rad/s
For a wave travelling in the +x direction the x and t terms have opposite signs: $y = A\sin(kx - \omega t)$
y = (0.02) m sin (7.85x – 1005t)
Note: the source prints '7.58x' in the first option; this is a misprint for 7.85x and has been corrected.
5 complete waves fit in 4 m, so $\lambda = \frac{4}{5} = 0.8$ m
Wave number: $k = \frac{2\pi}{\lambda} = \frac{2\times3.14}{0.8} = 7.85$ rad/m
Angular frequency: $\omega = vk = 128\times7.85 = 1005$ rad/s
For a wave travelling in the +x direction the x and t terms have opposite signs: $y = A\sin(kx - \omega t)$
y = (0.02) m sin (7.85x – 1005t)
Note: the source prints '7.58x' in the first option; this is a misprint for 7.85x and has been corrected.