Physics Wave Question (Urgent)

2013-05-08 7:53 pm

A transverse wave on a string is described by the wave function
y(x, t) = 0.332 sin(2.15x + 92.6t)
where x and y are in meters and t is in seconds. Consider the element of the string at x = 0.

(a) What is the time interval between the first two instants when this element has a position of y = 0.175 m?

(b) What distance does the wave travel during the time interval found in part (a)?

I want the steps and answer plz....

回答 (1)

天同

2013-05-08 11:59 pm

✔ 最佳答案

(a) Angular frequency w = 92.6 s^-1
hence, period T = 2.pi/92.6 s = 0.06785 s

At x = 0 m, the wave equation becomes: y = 0.332.sin(92.6t)
Hence, 0.175 = 0.332.sin(92.6t)
92.6t = arc-sin(0.175/0.332) = 31.81 degrees = 0.5552 radians
The first instant occurs at t = 0.5552/92.6 s = 6x10^-3 s
The second instant occurs when 92.6t = (180 - 31.81) degrees = 2.586 radians
i.e. at t = 2.586/92.6 s = 0.02793 s
Therefore, time interval = (0.02793 - 0.006) s = 0.02193 s

(b) since 2.pi/入 = 2.15
where 入 is the wavelength
hence, 入 = 2.pi/2.15 m = 2.922 m

Speed of wave = 入/T = 2.922/0.06785 m/s = 43.07 m/s
Distance travelled by wave = 43.07 x 0.02193 m = 0.944 m

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