https://general.physics.rutgers.edu/gifs/CJ/17-15.gif The arrangement in the dra

Question

https://general.physics.rutgers.edu/gifs/CJ/17-15.gif

The arrangement in the drawing shows a block (mass = 15.2 kg) that is held in position on a frictionless incline by a cord (length = 0.580 m). The mass per unit length of the cord is 1.28 × 10-2 kg/m, so the mass of the cord is negligible compared to the mass of the block. The cord is being vibrated at a frequency of 150 Hz (vibration source not shown in the drawing). What is the smallest angle between 15.0 ° and 90.0 ° at which a standing wave exists on the cord?

Explanation / Answer

Given that

The mass of the block is (m)=15.2kg

The length of the cord is (L) =0.580m

The linear density of the cord(u) =1.28*10-2kg/m

The frequency of the vibrating cord is(f) =150Hz

Nowthe tension in the string is given by

T =mgsintheta =(15.2)(9.81)sintehta =(149.112)sintheta

Then the velocity of the string is v =Sqrt(T/u)

The frequency of the string is f =nv/2L =(n/2L)Sqrt(T/u)

150 =(n/2*0.580)Sqrt(149.112sintheta/1.28*10-2kg/m)

22500=0.7431n2* (149.112sintheta/1.28*10-2kg/m)

22500=8655.485n2*sintheta

Sintheta =22500/8655.485n2 =2.599/n2

Where n=1,2,3,.....

Now n=2 ===>sinthea =2.599/4 then theta =40.532degrees

and for n =3 ===>sintheta =2.599/9 then theta =16.784degrees

the smallest angle between 15.0 ° and 90.0 ° at which a standing wave exists on the cord is 16.784degress

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