Question

A sonometer wire resonates with a given tuning fork forming standing wave with 5 antinodes between two bridges when mass of 9 kg is suspended from the wire. When mass 'M' is suspended from the wire, with same fork and same length between two bridges 3 antinodes are formed. Mass M is ______.

Options

• 25 kg

• 10 kg

• 15 kg

• 20 kg

Answer 1

A sonometer wire resonates with a given tuning fork forming standing wave with 5 antinodes between two bridges when mass of 9 kg is suspended from the wire. When mass 'M' is suspended from the wire, with same fork and same length between two bridges 3 antinodes are formed. Mass M is 25 kg.

Explanation:

Frequency of vibration of string, n = `"P"/(2"l") sqrt("T"/"m")`

Where m is linear mass density Case I: 

Number of loops (P₁) = Number of antinodes 

= 5

` therefore "n"_1 = 5/(2"l") sqrt("T"_1/"m")`

` therefore "n"_1 = 5/(2"l") sqrt((9"g")/"m")`  ...(i)

Case II:

Number of loop (P₂) =Number of antinodes =3

` therefore "n"_2 = 3/(2"l") sqrt("T"_2/"m")`

` therefore "n"_2 = 3/(2"l") sqrt("Mg"/"m")` ...(ii)

Dividing equation (i) and (ii),

`"n"_1/"n"_2 = (5 xx sqrt(9))/(3 xx sqrt("M")`

Since n₁ = n₂

` therefore 9 xx "M" = 25 xx 9`

`therefore "M"` = 25 kg