In a sonometer by what change in linear density of wire its velocity becomes double? Keeping tension of wire constant

Explanation:

In a sonometer , expression for speed of wave produced can be given as follows .

v =

v is velocity , T is tension in wire , m is density per unit length .

Here v is inversely proportional to square root of m . So if m becomes m / 4

velocity changes as follows .

velocity =

=

= 2v

velocity becomes two times . Hence to make velocity two times , mass per unit length  has to be changed to one fourth value , keeping tension constant .

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2