350 Transverse Vibrations of a Stretched Indiarubber Cord, 



Table showing Relation between the stretched Length of an 

 Indiarubber Cord and the corresponding Value o£ Young's 

 Modulus. 



Natural dimensions of the cord 9*3 cm. x *22 cm. x '221 cm. 

 Frequency of the stretched cord = 93. 



Original 

 Length 

 in cms. 



Final 



Length 



in cms. 



(L). 



Sectional 

 Area in 

 sq. cms. 



Increment 



of Tension 



in grams 



weight. 



Young's 



Modulus. 



(Y). 



Y 



L 2 ' 



26 



27 



•01 59 



16 



16 



26163 

 30270 



35-9 

 36-0 



28 



29 -0148 



30 



31 -0138 16 

 33 -0128 16 

 35 -0121 16 

 37 '0112 16 

 39 -01057 16 

 41 -0101 16 

 43 -0097 16 



45 -0094 16 



46 -00927 16 



34782 36-2 

 40000 36-7 

 44958 367 

 51200 37-3 



32 



34 



36 



38 ... 



40 



42 



57508 

 63366 

 69278 

 74734 

 78431 



37'8 

 37"6 

 374 

 36-9 

 37-0 



44 



45 













If this relation is borne in mind, it can be shown that the 

 frequency of a greatly stretched rubber cord will increase 

 very slowly indeed with increase of tension. 

 Let T= tension. 



I = natural length of the cord. 



L= stretched ,, „ 



m= mass of unit length of cord. 



w= mass of cord. 



p = density of the rubber. 



s = sectional area of the cord. 



Y= Young's modulus. 

 Then between the limits previously specified, 



s - 1 L* 



But psli = iv; 



dT v dh 



r w L 2 



Now since it has been shown that 



Y=*L 2 ; 



.*. p — =k.dL ; 



Pt- 



w 



T=£L + 0* 



* This assumes p constant. Villari found the density of rubber which 

 was stretched four times its natural length to be *966 times its natural 

 density. 



