Question

the frequency of a string depends on
length of vibrations segment (L)
tension of the vibration segment (F)
Mass per unit length (m)show that n proportional 1/2root F/m​

Answer 1

Answer:

Let the relation be:

Frequency v = KL

a

f

b

m

c

where k is a dimensionless constant

The dimension of each quantity are:

L=[M

0

L

1

T

o

]

f=[M

1

L

1

T

−2

]

m=[M

1

L

−1

T

0

]

v=[M

0

L

0

T

−1

]

Thus now equating the dimension on both side of the equation:

[M

0

L

0

T−1]=[M

0

L

1

T

0

]

a

[M

1

L

1

T

−2

]

b

[M

1

L

−1

T

0

]

c

thus, b=

2

1

c=−

2

1

a=−1

Thus the formula for frequency is:

V=

L

K

m

f