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Chapter 16: Q. 57 (page 453)

FIGURE P16.57 shows a snapshot graph of a wave traveling

to the right along a string at 45 m/s. At this instant, what is the

velocity of points 1, 2, and 3 on the string?

Short Answer

Expert verified

The speed of point 1,2 and 3 are-19m/s,0and19m/srespectively.

Step by step solution

01

given information

Speed of wave, v=45m/s.

Now, the distance between one complete wave that is the wavelength of the wave is, v=30cm=0.3m

Amplitude of the wave, according to the diagram,A=2cm=0.02m

02

Speed of point 1, 2 and 3

Speed of point 1 and 3 are equal in magnitude and directed opposite. Also, at crest or trough, the speed of any particle remains zero.

Now, the angular frequency,

蝇=2蟺惫位蝇=2蟺脳45m/s0.03m蝇=300蟺rad/s

Therefore, the speed of point 1 and 3 are,

v1=v3=vmax=蝇A鈬�vmax=300蟺rad/s0.02m鈬�v1=v3=19m/s

Thus, if we considerv1=-19m/sthenv3=19m/s.

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