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BITSAT 2022 Solved Question Paper
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© examsnet.com
Question : 4
Total: 130
Transverse waves of the same frequency are generated in two steel wires
A
and
B
. The diameter of
A
is twice that of
B
and the tension in
A
is half that in
B
. The ratio of the velocities of the waves in
A
and
B
is
1:2
1
:
√
2
1
:
2
√
2
3
:
2
√
2
Validate
Solution:
👈: Video Solution
The velocity if transverse waves is given by
v
=
√
T
m
where,
T
=
Tension and m = mass per unit
length of the wire. If r is the radius if the wire and ρ its density then,
m
=
π
r
2
ρ
∴
v
=
√
T
m
=
√
T
π
r
2
ρ
∴
v
A
=
√
T
A
r
A
√
π
ρ
and
v
B
=
√
T
B
r
B
√
π
ρ
Now,
v
a
v
B
=
√
T
A
T
B
.
r
B
r
A
∵
r
A
=
2
r
B
and
T
A
=
1
2
T
B
Hence,
v
A
v
B
=
1
2
√
2
© examsnet.com
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