Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is 
, and that in the other string having radius of cross section 
is 
. Then 
Text Solution
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To find the ratio of the velocities of transverse waves in two strings with different radii but identical materials and tension, consider the following:
The wave velocity 
in a string is given by the formula:
where 
is the tension and 
is the linear mass density of the string, defined as:
Here, 
is the density of the material, and 
is the radius of the string. Given that both strings have the same tension 
and material, we compare their wave velocities 
and 
for radii 
and 
.
The velocity ratio is expressed as:
Simplifying this expression:
Thus, the ratio 
is 2.
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