Given,

Speed of the pulse along a spring , v = 14.4 m/s

Frequency of the spring, f  = 5.2 Hz

For three loop standing wave:

Length of the spring , L =(3/2) 𝛌 

Wave length of the spring 𝛌 =(2/3)L

Calculate the  length of the spring by using the standard wave equation.

f  = (1/𝛌) v

Substitute (2/3)L  for 𝛌.

f  = (1/((2/3)L)) v

f = (3/2) (1/L) v

L=(3/2) (1/f ) v

  =(3/2) (1/5.2)14.4

  =4.154 m

Therefore , the length of the spring is 4.154 m