A light string with the linear density of 8g/m has its ends tied to two walls se

Question

A light string with the linear density of 8g/m has its ends tied to two walls separated by a distance equal to

A light string with the linear density of 8g/m has its ends tied to two walls separated by a distance equal to 3/4 the length of the string. An object of mass m is suspended from the center of the string, putting a tension in the string. Find an expression for the wave speed in the string that depends only on given quantities. What should be the mass of the suspended object if the wave speed is to be 60m/s? Be sure to show all forces in the sketch below as well as a free body diagram for the object of mass m.

Explanation / Answer

A.

Standard wave equation;

Y=Asin(kx-wt)

Now from given situation;

2Tcos(theta)=mg

where theta is the angle made by rope with vertical;

or

T=0.5mg/cos(theta)

Also the velocity of wave is given by;

v=sqrt(T/u); where u is mass per unit length of the rope;

B.

using;

v=sqrt(T/u)=v=sqrt(.5mg/cos(theta)*u)

From diagram;

sin(theta)=(6/8)

or

theta=48.59

hence;cos(theta)=0.6614

so

m=3.884kg

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