COMEDK 2024 Shift 1 Paper

To solve for the minimum value of ∆t that allows for constructive interference between successive pulses, we must determine the time it takes for a wave pulse to travel from one end of the string to the other and back. This time is essentially the period for which constructive interference will occur.
First, we find the wave speed, v, on the string. The wave speed is given by the formula:
v=√‌

T

µ

where:
T is the tension in the string, which is given as 2.5 N . µ is the linear mass density of the string.
The linear mass density µ can be calculated using the formula:
µ=‌

m

L

Where:
m is the mass of the string, given as 10−3‌kg.
L is the length of the string, given as 25 cm (which we convert to meters as 0.25 m ).
Thus,
µ=‌

10−3‌kg

0.25m

=4×10−3‌kg∕m
Now, substituting µ and T back into the wave speed formula:
v=√‌

2.5N

4×10−3‌kg∕m

=√625m2∕ s2=25m∕ s
Now that we have the wave speed, we can calculate the time it takes for the wave pulse to travel the length of the string and back (i.e., a round trip). The total distance for a round trip is 2L, so the time interval ∆t is given by:
∆t=‌

2L

v

Substituting the given values:
∆t=‌

2×0.25m

25m∕ s

=‌

0.5m

25m∕ s

=0.02 s=20‌ms
Thus, the minimum value of ∆t for constructive interference between successive pulses is: Option D: 20 ms