Question 230: Waves

Question

An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man can hear the frequency up to 19.5 kHz , Neglect end correction)

Accepted Answer

Organ pipe closed at one end
Fundamental frequency = $f_1 = 1500 \,	ext{Hz}$.
Hearing limit = $19.5 \,	ext{kHz} = 19,500 \,	ext{Hz}$.
Neglect end correction.
Step 1: Harmonics of a closed pipe
For a closed organ pipe:
$ f_n = (2n-1) f_1, \quad n = 1,2,3,\dots $
So allowed frequencies are odd multiples of the fundamental.
That means the sequence is:
$ f_1 = 1 \cdot 1500 = 1500,   f_3 = 3 \cdot 1500 = 4500,   f_5 = 7500,   f_7 = 10{,}500,\ \dots $
Step 2: Find maximum $n$
We require $(2n - 1) \cdot 1500 \leq 19500$.
$ 2n - 1 \leq \frac{19500}{1500} $
$ 2n - 1 \leq 13 $
$ 2n \leq 14 \quad \Rightarrow \quad n \leq 7 $
So the
highest harmonic is the 13th (when $2n-1 = 13$)
.
Step 3: Count overtones
Fundamental (1st harmonic) = 1500 Hz.
Next one (3rd harmonic) = 4500 Hz =
1st overtone
.
Then 5th harmonic =
2nd overtone
, and so on.
Up to 13th harmonic =
6th overtone
.
Ã¢ÂÂ Final Answer:
The maximum number of overtones audible is
6
.
Correct Option: A (6)

Answer

6

Answer

3

Answer

13

Answer

11

Waves

An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man can hear the frequency up to 19.5 kHz , Neglect end correction)

Choose the correct answer: