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Contact [7]
3 years ago
7

An organ pipe open at both ends has two successive harmonics with frequencies of 220 Hz and 240 Hz. What is the length of the pi

pe? The speed of sound is 343 m/s in air.
Physics
1 answer:
Harman [31]3 years ago
7 0

Answer:

The  length is  l  =  8.6 \  m

Explanation:

From the question we are told that

   The frequencies of the two successive harmonics are f_1 =  220 \ Hz ,  f_2  =  240 \  Hz

   The speed of sound in the air is  v_s  =  343 \  m/s

Generally the frequency of a given harmonic is mathematically represented as

     f_n  =  \frac{n  v  }{2l}

Here  n defines  the position of the harmonics

Now since the position of both harmonic is not know but we know that they successive then we can represented them mathematically as

    220  =  \frac{n v}{2l}

and  

     240  =  \frac{(n+1) v}{2l}

So

   \frac{(n + 1 ) v}{2l} - \frac{n v}{2l}  =  240-220

=>  \frac{v}{2l}  =  20

=>   l  =  8.6 \  m

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