The displacement of a string is given by The wavelength of the wave is:
A) 2 $\pi$k/ $ \omega $
B) k/ $ \omega $
C) $ \omega $k
D) 2 $\pi$/k
E) k/2 $\pi$

Question

The displacement of a string is given by  The wavelength of the wave is:
A) 2 $\pi$k/ $ \omega $ 
B) k/ $ \omega $ 
C) $ \omega $k 
D) 2 $\pi$/k 
E) k/2 $\pi$

Quizplus · Accepted Answer

The displacement of the wave can be written as:
y(x,t) = A sin(kx - w t)
where k is the wave number and w is the angular frequency.

Comparing with the given displacement:
11eaafc0_2fc5_dfb8_a7a5_ad831dcef140_TB3977_00 = A sin(kx - w t)

Since we don't have values for either A, x or t, we cannot solve for k or w directly. However, we know that in one complete wavelength, the displacement of the wave repeats itself. Therefore, we can find the wavelength as the distance over which the function repeats itself.

The general formula for the wavelength is given by:
wavelength = 2π/k

Comparing with the given options, we can see that option D matches this formula:
wavelength = 2π/k     (Option D)

Therefore, the answer is D.

The Displacement of a String Is Given by the Wavelength