Question

Wire having tension 225 N produces six beats per second when it is tuned with a fork. When tension changes to 256 N, it is tuned with the same fork, the number of beats remain unchanged. The frequency of the fork will be ______.

पर्याय

• 186 Hz

• 225 Hz

• 256 Hz

• 280 Hz

Answer 1

Wire having tension 225 N produces six beats per second when it is tuned with a fork. When tension changes to 256 N, it is tuned with the same fork, the number of beats remain unchanged. The frequency of the fork will be 186 Hz.

Explanation:

The fundamental frequency of vibrating wire is given by

f₁ = `1/2sqrt("T"/mu)`

Here, µ = mass of string per unit length

T = tension in the wire

Let x be the frequency of tunning fork according to question

(x - f) = ±6

∴ f₁ = `1/(2"L")sqrt(225/mu)` and f₂ = `1/(2"L")sqrt(256/mu)`

∴ `"f"_1/"f"_2=15/16`

⇒ f₂ = `16/15xx"f"_1`

⇒ f₂ = `16/15(6+"x")`

Equating the two cases of f₁ we have

(x + 6)=`16/15("x"-6)`

∴ 15x + 90 = 16x - 96

∴ x = 186 Hz