Question

The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by 69%, keeping the length constant. The frequency of the wire is ______.

Options

• 42 Hz

• 24 Hz

• 30 Hz

• 36 Hz

Answer 1

The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by 69%, keeping the length constant. The frequency of the wire is 30 Hz.

Explanation:

We know that, frequency of vibration of a stretched string is given by 

v = `1/"2l" sqrt("T"/"m")`

where, T = tension in string

m = mass/length

and I = length of string.

New frequency,

v' = `"v" + 9 = 1/(2"l") sqrt(("T" + (69//100)"T")/"m")`

`=> "v"/"v'" = sqrt("T"/(169/100)"T")`

`=> "v"/("v + 9") = sqrt(100/169) = 10/13`

⇒ 13v = 10v + 90

v = 30 Hz