Question

20. A sonometer wire resonates
with a given tuning fork forming
standing waves with five antinodes
between the two bridges when a
mass of 9 kg is suspended from
the wire. When this mass is
replaced by a mass M, the wire
resonates with the same tuning
fork forming three antinodes for
the same positions of the bridges.
The value of M is​

Answer 1

Correct option is

A

25 kg

Frequency of vibration of vibration of string, n=

2l

p

m

T

No. of loops = No. of antinodes

For, p=5

T=9g

∴n

1

=

2l

5

m

9g

For, p=3

T=Mg

∴n

2

=

2l

3

m

Mg

n

1

n

2

∴

2l

5

M

9g

=

2l

3

m

Mg

⇒M=25 kg.