11Solved Numerical Problem No.13 ( Unit-8: Waves ); HSSC-1 (Class-11); Physics (New Book/KPK Text Board, Peshawar) With Verified Answers

What length of open pipe will produce a frequency of 1200 Hz as its first overtone on a day when the speed of sound is 340 m s⁻¹ (28.3cm)

Given:

Speed of sound = v = 340 m s⁻¹

Frequency of first overtone = f₂ = 1200 Hz

To Find:

Length of the open pipe = L =  ?

Solution:

Since for the first overtone 

f₂ = 2 f₁

But  f₁ = `\frac {v}{2 L}`

So   f₂ = 2 `\frac {v}{2 L}`

or 

f₂ =  `\frac {v}{L}`

or

L = `\frac {v}{f₂}`

by putting values

L = `\frac {340 m s⁻¹}{1200 Hz}`

L = 0.28333 m

0r 

L = 28.3 cm ----------------Ans

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