Question

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.