Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0700 m, and w

Question

Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0700 m, and wavelength 0.320 m. These waves travel in the x  direction, and at t = 0 the x = 0 end of the string is at y = 0 and moving downward

)A) Find the frequency of these waves.

25.0

B)Find the period of these waves.

4.00×102

C) Write the equation for y(x,t) describing these waves.

y(x,t) =____________________(m)

D)Find the transverse displacement of a point on the string at

x2 = 0.120 m at time t2 = 0.145 s .

y=_____________________(m)

25.0

Explanation / Answer

Solution: From the question we have:

Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0700 m, and wavelength 0.320 m

These waves travel in the x  direction, and at t = 0 the x = 0 end of the string is at y = 0 and moving downward

a) Find the frequency of these waves.

A) f = v / = 8m/s / 0.320m = 25 Hz

b)Find the period of these waves

B) T = 1/f = 1 / 25/s = 0.04 s

c) Write the equation for y(x,t) describing these waves.

y = Asin(kx - t) = 0.07m * sin(19.6x - 157t)
since = 2f = 2*25 rad/s = 157 rad/s

d) Find the transverse displacement of a point on the string at

y = 0.07m * sin(19.6*0.12 - 157*0.145) =0.02441. m

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