Question

In an open organ pipe third harmonic is 450 Hz . what is the frequency of fifth harmonic

Answer 1

for third harmonic in open organ pipe is shown in figure.
λ/4 + λ/2 + λ/2 + λ/4 = L { length of organ pipe }
3λ/2 = L
λ = 2L/3 => frequency = 3c/2L { c is the speed of light }
hence, 3c/2L = 450 Hz -------(1)

similarly for 5th harmonic,
λ/4 + λ/2 + λ/2 + λ/2 + λ/2 + λ/4 = L
2λ + λ/2 = L
5λ/2 = L => frequency = 5c/2L
hence, frequency = 5c/2L -------(2)


divide equation (1) ÷ (2)
{3c/2L}/{5c/2L} = 450/frequency
3/5 = 450/frequency
frequency = 750 Hz

hence, frequency of 5th harmonic = 750 Hz

Answer 2

750 Hz will be the frequency of the fifth harmonic.

Explanation:

As we know,

ν(f) = nv/2L

n = any natural number

v = velocity

L = length

Now, n = 3

Frequency of third harmonic = 3v/2L/3

= 450/3

⇒ v/2L = 150

∵ Frequency of fifth harmonic;

n = 5

Frequency of fifth harmonic = 5v/2L

by putting (v/2L = 150)

= 5 * 150Hz

= 750Hz

Thus, the frequency of the fifth harmonic is 750Hz.

Learn more: Frequency

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