Standing waves on a string are generated by oscillations having amplitude 0.005

Question

Standing waves on a string are generated by oscillations having amplitude 0.005 m, angular frequency 942 rad/s, and wave number 0.750p rad/m.

a.) What is the equation of the standing wave?
b.) At what distances from x=0 are the nodes and antinodes?
c.) What is the frequency of a point on the string at an antinode?
d.) If the string is 4m long, how many nodes are there?

I've resolved that the equation for the standing wave is: y=.01sin(.750pix)cos942t for part a

But other than that im not sure how to start this

Explanation / Answer

y = 0.005*2 cos(942t)sin(0.750 x)

At Nodes

dy/dt = Maximum

=> d2y/dt2 = 0

=> 0.01 * 942 *942 -cos( 942 t ) sin [( 0.75 )x]( at t=0) =0

=> sin ( 0.75 x) = 0

=> 0.75 x = n where n = 0,1,2,3,4

x = n/0.75 = 4/3 *n 

b)

Hence nodes are at x= 4/3 , 8/3 , 4...

Wavelength =2( 4/3-0) = 8/3

=>  Position of first anti-node = /4 = 2/3

=> Position of second anti node =3/4 * = 3/4 * 8/3 = 2

Position of third anti node =5/4 * = 5/4 * 8/3 = 10/3

 

c)

Frequency at antinode = /2 = 942/2 = 149.92  Hz

d)

Nodes are at x =0,4/3, 8/3 and 4

Hence there are 4 nodes

------------------

Hope This will do/. :) 

 

 

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.