Question

A string is stretched with a tension of 120 N. The string has a length of 2.5 meters. The velocity of wave propagation along the string is 220 m/s. Calculate the mass per unit length of the string is?

Answer 1

Question :-

A string is stretched with a tension of 120 N. The string has a length of 2.5 meters. The velocity of wave propagation along the string is 220 m/s. Calculate the mass per unit length of the string .

Answer :-

Given :

Tension ( T ) = 120 N

Velocity ( v ) = 220 m/s

Length ( l ) = 2.5 m

mass ( m ) = ?

Now :

Apply the formula :

v = √( t / u )

where u = m / l ( mass per unit length )

v = √ ( t / u )

==> 220 = √ ( 120 / u )

Squaring both sides we get :

==> 48400 = 120 / u

==> u = 120 / 48400

==> u = 12 / 4840

==> u = 3 / 1210

Now :

m / l = u

==> m / 2.5 = 3 / 1210

==> m = 7.5 / 1210 m

==> m = 0.00619 m

==> m = 0.0062 m

or m = 0.62 cm

The mass of the string is 0.62 cm or 6.2 × 10⁻³ m

Correct me if I am wrong

Hope it helps

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