The following two waves are sent in opposite directions on a horizontal string s

Question

The following two waves are sent in opposite directions on a horizontal string so as to create a standing wave in a vertical plane, with x in meters and t in seconds. y(x, t) = (4.80 mm) sin(15pi x - 470pi x) y(x, t) = (4.80 mm) sin(15pi x + 470pi t) An antinode is located at point A. In the time interval that point takes to move from maximum upward displacement to maximum downward displacement, how far does each wave move along the string? The given functions are the standard form used for transverse waves in the chapter. Do you see that they move in opposite directions and have the same amplitude and thus form a standing wave given by Eq. 16-60? How much of a period is required for point A to move vertically by the stated amount? In terms of a wavelength, how far does a wave travel in that much time? Can you get wavelength from the wave number?

Explanation / Answer

for the time from maximum up to maximum down, time taken is half the time period.

and distance tarveled along the string is half the wavelength.

k = 2 pi / lambda

and k = 15 pi { wave eq: y = x sin(kx - wt) }

15 pi = 2pi / lambda

lambda =0.133 m

and d =lambda/2 = 0.0667 m Or 6.67 cm

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