NEET Class neet Answered
A travelling harmonic wave is represented by the equation y(x,t) = 10–3
sin (50t + 2x), where, x and y are in
mater and t is in seconds. Which of the following is a correct statement about the wave ?
(1) The wave is propagating along the positive x-axis with speed 100 ms–1
(2) The wave is propagating along the positive x-axis with speed 25 ms–1
(3) The wave is propagating along the negative x-axis with speed 25 ms–1
(4) The wave is propagating along the negative x-axis with speed 100 ms–1
Why is the wave propagating along negative direction please explain
Asked by nipunverma59 | 22 Jan, 2019, 08:16: PM
Expert Answer
I assume the given equation : y(x,t) = 10-3 sin(50t+2x) .........................(1)
The equation for a harmonic wave travelling in -ve x-diection : y(x,t) = a sin (ωt+Φ) ..............(2)
where ω = 2πf is angular frequency and f is the frquency of vibration at any point in the wave.
Φ = 2πx/λ is the phase of vibration at the location x and λ is the wavelength of wave.
hence eqn.(2) is rewritten as, y(x,t) = a sin[ 2πf t + (2πx/λ) ] ..............................(3)
By comparing eqn.(1) and eqn.(3), we have 2πf = 50 or f = 50/(2π) and ( π/λ ) = 1 or λ = π
Hence velocity : f×λ = [ 50/(2π) ]×π = 25 m/s
Since the phase term in the wave equation is +ve, the wave progress in -ve x -direction with velocity 25 m/s
Answered by Thiyagarajan K | 23 Jan, 2019, 03:16: PM
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