Question

When tension T is applied to a sonometer wire of length l, it vibrates with the fundamental frequency n. Keeping the experimental setup the same, when the tension is increased by 8 N, the fundamental frequency becomes three times the earlier fundamental frequency n. The initial tension applied to the wire (in newton) was ______.

पर्याय

• 2.0

• 2.5

• 0.5

• 1.0

Answer 1

When tension T is applied to a sonometer wire of length l, it vibrates with the fundamental frequency n. Keeping the experimental setup the same, when the tension is increased by 8 N, the fundamental frequency becomes three times the earlier fundamental frequency n. The initial tension applied to the wire (in Newton) was 1.0.

Explanation:

The initial fundamental frequency of wire,

n = `1/"2L" sqrt("T"/mu)`   ..(i)

The final fundamental frequency of wire,

n' = 3n = `1/"2L" sqrt(("T" + 8)/mu)`  ...(ii)

On dividing Eq. (ii) by Eq. (i), we get

`"3n"/"n" = (1/"2L" sqrt(("T + 8")/mu))/(1/"2L" sqrt("T"/mu))`

3 = `sqrt(("T + 8")/"T")`

⇒ 9T = T + 8

T = 1 N