Question

Five beats per second are heard when a tuning fork is sounded together with a sonometer wire when its length is either 95 cm or 100 cm then the frequency of the tuning fork is

Answer 1

5 beats/second are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will  150 Hz

Answer 2

Let us take the frequency of the tuning fork as f.

When sonometer sounded together with the fork,

λ$λ/2=l\\\\λ=2l$

When we apply $V=fλ$

$V=f X 2l\\\\f=V/2l$ ---------------(1)

$λ=Wave Length$

$l=length$ of sonometer wire

When $l=95cm$,

By equation (1),

f1 = V/2 X 0.95

f1 = V/1.9

When $l=100cm$,

By equation (1),

f2 = V/2 X 1

f2 = V/2

$Beats =|f - F |$ -----------(2)

We can see that f1 > f2

Then we can derive below from (2),

5 = f1 - f

5 = (V/1.9) - f

9.5 = V - 1.9f ------------------------(3)

5 = f - f2

5 = f - V/2

10 = 2f-V ------------------------------(4)

(3) + (4),

19.5 = 0.1f

f = 195 Hz