Two similar sonometer wires of same material produce beat of 2hz. The length of one wire is 150cm and the other is 50.1cm. Calculate the frequencies of two wires

Answer 1

Given that the two sonometer wires are producing a beat frequency of 2 Hz.

Let the frequency of the longer wire be f1, and the frequency of the shorter wire be f2.

The beat frequency is given by:

Beat frequency = f1 - f2 = 2 Hz

Next, we can calculate the frequencies of the two wires:

Let the speed of sound in the wire be v m/s.

For the longer wire:
f1 = v / λ1 = v / 2L1
where L1 = 150 cm = 1.5 m

For the shorter wire:
f2 = v / λ2 = v / 2L2
where L2 = 50.1 cm = 0.501 m

Substitute f1 and f2 into the formula for the beat frequency:

(v / 2L1) - (v / 2L2) = 2
v(1 / 2L1 - 1 / 2L2) = 2
v(1 / 3 - 1 / 3.002) = 2
v = 997.5064 m/s

Now, calculate the frequencies f1 and f2:

f1 = v / 2L1 = 997.5064 / (2 x 1.5) = 332.5021 Hz
f2 = v / 2L2 = 997.5064 / (2 x 0.501) = 665.0042 Hz

Therefore, the frequencies of the two sonometer wires are approximately 332.5021 Hz and 665.0042 Hz.