1. (P3 4-7) For a harmonic wave given by y = (10cm) * sin [ (628.3/cm)*x-(6283/s

Question

1. (P3 4-7) For a harmonic wave given by y = (10cm) * sin [ (628.3/cm)*x-(6283/s) (a) wavelength (b) frequency (c) propagation constant (d) angular frequency (e) period (f) velocity (g) amplitude , determine 2. (P3 4-8) For the three following expressions, determine whether the equation represents a traveling wave (please note that we're just asking whether it's a traveling wave, not whether it's a periodic or harmonic one). If the equation represents a traveling wave, please determine its travel/propagation velocity in terms of the constants A, B, C and D (either by using the constant phase condition, or simply by changing the phase expression into a particularly suitable format). Distances are in meters and time in seconds. (a) fly.t) -Aly-Bt) (b) ffx,t) - A(BCt D)

Explanation / Answer

Q1:

Equation of wave is given by:

y=Asin(kx-wt)------------equation (1)

where A is amplitude, k is propagation constant , x is the displacement, w angular frequency, t is time.

Now equating the given equation with equation (1)
y =(10 cm)*sin[(628.3/cm)*x-(6283/s)*t]
y=Asin(kx-wt)

We get,
Amplitude= 10 cm.
propagation constant=628.3/cm
angular frequency=6283/s

Now angular frequency(W)=2^n where n is the frequency

n=w/(2pie)

Substituting "w" we get

n=6283/(2*(22/7))
=999.9=1000/s(frequency)

Also k=2Pie/Wavelength
  
Wavelength=2Pie/k
=0.0100432= 4.3*10^(-5) cm

Also Time Period= 1/Frequency
=1/1000
=1* 10^(-3)=1ms

Also Amplitude is given as,
velocity=frequency * wavelength
=1000*4.3*10^(-5)
=4.3*10^(-2) cm/s

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