Ratio reasoning Two ropes have equal length and are stretche

Ratio reasoning Two ropes have equal length and are stretched the same way.The speed of a pulse on rope 1 is 1.4 times the speed on rope. Determine the ratio of the masses of the two ropes (m_1/m_2).

Solution

speed of wave = sqrt (T/u)

where T is tension and u is mass per unit length

=> v1/v2 = sqrt ( M2/M1)

=> 1/4 =  sqrt ( M2/M1)

=> M2/M1 = 1/16

=> M1/M2 = 16