Module 3C: Interference of Waves 7. Two sinusoidal waves with the same amplitude

Question

Module 3C: Interference of Waves 7. Two sinusoidal waves with the same amplitude of 9.00 mm and the same wavelength travel together along a string that is stretched along an x axis. Their resultant wave is shown twice in the figure, as valley A trav- els in the negative direction of the x axis by distance d 56.0 cm in 8.0 ms. The tick marks along the axis are separated by 10 cm, and height H is 8.0 mm. Let the equation for one wave be of the form y(x, t) = I'm sin(kx ±at +4), where -0 and you must choose the correct sign in front of o. For the equation for the other wave, what are (a) ym , (b) k, (c) a) , (d) , and (e) the sign in front of Hint: To solve this problem you will need a clear understanding of the physical meaning of wave speed, wave length, amplitude, and the resultant of wave interference so that you may read some of the data from the graph.

Explanation / Answer

(a)

y m of the wave is = 9.0 mm

(b)

from the graph

lamda = 4(10 cm) = 40 cm = 0.4 m

k = 2pi/ lamda = 2pi/0.4 = 15.7 m^-1

(c)

v= 56cm/8* 10^-3 s = 0.56 m/0.008 = 70 m/s

w= kv = 15.7(70) = 1099 rad/s

(d)

amplitude of resultant wave = H/2 = 4.0 mm = 2ymcos(2/2) = 2*9.0cos(2/2) ( take calcualtor in radian mode)

2 = 2.6893rad

(e)

since waave is travelling in negative x direction the sign of w is positive

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