### Frequency

The definition of frequency, we can understand that if a body is in periodic motion, it has undergone one cycle after passing through a series of events or positions and returning to its original state. Thus, frequency is a parameter that describes the rate of oscillation and vibration.

The relation between the frequency and the period is given by the equation:

f=1/T

**Given**

String is stretched between fixed point separated by the distance = 75 cm

Therefore, L = 75cm

The resonant frequencies of 420 Hz and 315 Hz.

**Find out**

We have to determine the lowest resonant frequency for this string

**Solution**

For the string fixed at both the ends, resonant frequency are given by f = nv/2L

Where,

n = smallest integer

v = velocity of sound

L = separation length of the string by which it is stretched.

Given that 315 Hz and 420 Hz are two consecutive resonant frequencies, let these be nth and (n + 1)th harmonics.

315 = nv/2L ——-(i)

420 = (n+1)v/2L——–(ii)

On dividing equa (i) by equation (ii) we get

n = 3

From equa (I), we get

lowest resonant frequency

f_{0} = v/2L

= 315/3

= 105 Hz

**Answer**

The lowest resonant frequency for this string is 105Hz

**Check out the video given below to know more about resonance frequency**

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