Question

What is the base frequency if a pipe gives notes of frequency $425,255$ and $595$ and decides whether it is closed at one end or open at both ends?
A. $17,closed$
B $85,closed$
C. $17,open$
D. $85,open$

Answer 1

Hint:We need to know the full concept of close pipe and open pipe then the only way you can solve this problem easily. First assuming it as a close pipe using the close pipe concept you will come to know the base frequency now with the help of that base frequency we can generate the relation with the given frequency.

Complete step by step answer:
Open pipe: It is a pipe that is open at both the ends and a standing wave can form if the wavelength of the sound allows there to be an antinode.
Close pipe: But in this one end is open and the other is closed similarly here also standing waves with sound of an appropriate frequency.

As per the given problem, three notes of frequency are given $ = 425,255$ and$595$. Now let us assume that the base frequency is $n$ that base frequency is for a closed pipe. As we know the concept of close pipe is that notes of close pipe are $n,3n,5n$ etc. As in the problem three notes of frequency is given applying these frequency in close pipe concept we get,
$255 = 3n$
$ \Rightarrow n = \dfrac{{255}}{3}$
$ \Rightarrow n = 85$
Hence we get the base frequency as $85$ .

Now with the help of this base frequency we can compare the other two given frequencies.
Here,
$5n = 425$
This is because,
$5 \times 85 = 425$
Similarly,
$7n = 595$
This is because,
$7 \times 85 = 595$
Hence from the above discussion we conclude that the base frequency is for a close pipe with base frequency $85$ .

Therefore the correct option is $\left( B \right)$.

Note:Generally this type of question is logical, we have to analyse the given frequency and have to assume the pipe and the second important in this is proper comparison of given frequency with the assumed pipe. If your assumption is wrong then the alternate one will be correct and once cross check it with another pipe if your assumption is wrong before choosing the option.