Answered: 2. The mathematical representation of a…

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter18: Superposition And Standing Waves

Section: Chapter Questions

Problem 18.25P: A certain vibrating string on a piano has a length of 74.0 cm and forms a standing wave having two...

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2. The mathematical representation of a standing wave is... y = (0.5m)sin(3πt)sin(2πx) , with x in meters and t in seconds. What is the x-coordinate of the antinode closest to the origin (x > 0)?

	a.	0.125 m
	b.	0.167 m
	c.	0.250 m
	d.	0.333 m

Expert Solution

Step 1

HINT:)

for a standing wave of the form

y=A*sin(kx)cos(wt) (w:ohmega)

antinode occurs when

$\sin (k x) = \pm 1$
i.e $k x = \frac{π}{2}, \frac{3 π}{2}$ ....

where $k = \frac{2 π}{λ}$
so closest antinode would be

kx= $\frac{π}{2}$

or $\frac{2 π}{λ}$ x= $\frac{π}{2}$

$x = \frac{λ}{4}$

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