To determine the time taken by the wave pulse to travel along the wire from point
P to
R, we first need to calculate the speed of the wave in each segment of the wire (
PQ and
QR ) and then find the time taken to travel through each segment.
We have two wires
PQ and
QR with different lengths and masses but the same radius and therefore the same cross-sectional area
A. Both wires are under the same tension T. Given that the tension and cross-sectional area are the same for both wires, we can assume that the linear density (mass per unit length) is different because they have different masses and lengths.
To find the linear density
(µ) for each wire, we use the formula:
µ=‌where
m is the mass of the wire, and
L is the length of the wire.
For wire
PQ :
µPQ=‌=‌=0.0125‌kg‌/‌mFor wire
QR :
µQR=‌=‌=0.078125‌kg‌/‌m The speed of a wave in a stretched string or wire is given by the formula:
v=√‌where
v is the speed of the wave, and
T is the tension in the wire.
Using this formula, we can calculate the speed of the wave in each section of the wire.
For wire
PQ :
vPQ=√‌=√‌=√6400m2/ s2=80m/ sFor wire QR:
vQR=√‌=√‌=√1024m2/ s2=32m/ s Now we will find the time taken for the wave to travel through each section.
Time is distance over speed, so for wire
PQ :
tPQ=‌=‌=0.06 sAnd for wire
QR :
tQR=‌=‌=0.08 s To find the total time taken by the wave pulse to travel from
P to
R, we add the times for
PQ and
QR :
t‌total ‌=tPQ+tQR=0.06s+0.08s=0.14sThe correct answer is:
Option C:
0.14 s