Physics

1. Physics 101 Learning Object
Does pulse speed change on a vertical string?
Question: Instead of a horizontal string, a string of length, L, is hanging from the
ceiling with a mass, M. When a disturbance generates a pulse from the lower
end, how does the speed of the pulse change as it moves higher towards the
ceiling? Would you expect the speed to increase, decrease, or stay the same as
the pulse moves upwards? What factors determine the pulse speed and how
does the equation for pulse speed change when it becomes vertical?
Answer: You would expect the pulse speed to increase as the transverse wave moves
upwards towards the ceiling.

2. Explanation: To determine pulse speed on a string horizontally, we can use the two
equations:
where F in this case is equal to the tension force (T) acting upon the string. However, in
a case where it is vertical, there is more than just tension force, as gravity and weight of
the mass now also needs to be considered.
Referring to the free body diagram above with the mass on a string, the net force is
equal to tension (assume upwards force is positive) subtracted by the weight of the
mass (assume downwards force is negative). This is given by:
Fnet= T-mg= ma (where a is assumed to be g=9.81 m/s^2)
Moving the terms over to isolate tension,
T= ma + mg
In this case, the term mg is equal to the mass of the block times gravity. For ma,
however, the mass can be substituted by:
μ= M/L ——> M= μL ——> M=μx (where x is the height of the point
measured from the bottom of the string)
Substituting for the force in the pulse speed equation,
v(x), we get:
From the above equation, as x gets higher (as the pulse travels higher on the string), it
is clear that the speed increases.