Question 4
The velocity v of a wave ina stretched string depends on the tension, T, in the spring and the mass per unit length μ of the spring. Obtain an expression for v in terms of T and μ, using the method dimensions.
Observation
This question was unpopular among candidates and the performance of the few that attempted it was poor.
The expected answer is:
Expression for v
vα Tamb OR
v = kTamb, k is dimensionless
[v] = k[T]a[m]b
LT-1 = k(MLT-2)a(ML-1)b
LT-1 = kMa + bLa – bT-2a
For T,
-1 = -2a
a = ½
For M,
0 = a + b
b = -a
= -½
v = kT½m-½
OR
v = k