The equation of a simple harmonic progressive wave is
Where y and x are in cm and t in second. Calculate the amplitude, frequency and speed of the wave and the phase difference between two particles at a distance of 2.0 cm apart at any instant.
Amplitude = 8cm, frequency = 2.0 s–1, wave speed = 20 cm/s & phase difference = 72o.
The equation of the wave is
Comparing it with the standard equation we get
amplitude a = 8 cm
time-period T = (1/2)s
Wavelength λ = (1/0.1) cm = 10 cm.
If the distance between two points is âˆ†x, then the phase difference between them is given by
Here λ = 10 cm and âˆ†x = 2.0 cm.
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In the figure given below is shown displacement-distance (y – x) graph of a transverse wave travelling along a string at the instant t = 0.25 s. At the instant t = 0, the end A of the string was in the mean position. Find out: (i) Frequency, wave-length and velocity of the wave, (ii) Equation of the wave, (iii) Displacement of B at the instant t = 1 second.
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