
A standing wave propagating with velocity $ 300m/s $ in an open pipe of length $ 4m $ has four nodes. The frequency of the wave is?
(A) $ 75Hz $
(B) $ 100Hz $
(C) $ 150Hz $
(D) $ 300Hz $
(E) $ 600Hz $
Answer
460.2k+ views
Hint : To solve this question, we need to find out the length of the pipe in terms of the wavelength with the help of the number of nodes given in the question. For this we have to draw the diagram of the nodes and antinodes in an open pipe and from that we can easily find out the relation. Then, we have to use the relation between the frequency and the wavelength to get the final answer.
Formula Used: The formula which is used to solve this question is given by
$\Rightarrow \lambda f = v $ , here $ \lambda $ is the wavelength, $ f $ is the frequency, and $ v $ is the velocity of a wave.
Complete step by step answer
Let the frequency of the wave be $ f $ .
According to the question, we have an open pipe in which a standing wave has four nodes. So, this situation can be represented by the below diagram.
As we know that the distance between a node and an antinode is equal to one fourth of the wavelength of the light, so the total length of the pipe becomes
$\Rightarrow L = 8\left( {\dfrac{\lambda }{4}} \right) $
$ \Rightarrow L = 2\lambda $
Dividing both the sides by $ 2 $ , we get
$\Rightarrow \lambda = \dfrac{L}{2} $
According to the question, the length of the pipe is $ 4m $ . Therefore substituting $ L = 4m $ above we get
$\Rightarrow \lambda = \dfrac{4}{2} = 2m $ (1)
So the wavelength of the wave is equal to $ 2m $ .
Now, we know that the frequency and the wavelength of a wave are related by the relation
$\Rightarrow \lambda f = v $
So the frequency of the wave is given by
$\Rightarrow f = \dfrac{v}{\lambda } $
According to the question, $ v = 300m/s $ . Also, from (1) we have $ \lambda = 2m $ . Substituting these above we get
$\Rightarrow f = \dfrac{{300}}{2} $
$ \Rightarrow f = 150Hz $
Thus the frequency of the wave is equal to $ 150Hz $ .
Hence, the correct answer is option C.
Note
We need to be clear with the terminology of the organ pipes. An open organ pipe is a pipe which is closed at both the ends. While a closed organ pipe is closed only at one end. It must be noted that at least one end of the organ pipe must be open.
Formula Used: The formula which is used to solve this question is given by
$\Rightarrow \lambda f = v $ , here $ \lambda $ is the wavelength, $ f $ is the frequency, and $ v $ is the velocity of a wave.
Complete step by step answer
Let the frequency of the wave be $ f $ .
According to the question, we have an open pipe in which a standing wave has four nodes. So, this situation can be represented by the below diagram.

As we know that the distance between a node and an antinode is equal to one fourth of the wavelength of the light, so the total length of the pipe becomes
$\Rightarrow L = 8\left( {\dfrac{\lambda }{4}} \right) $
$ \Rightarrow L = 2\lambda $
Dividing both the sides by $ 2 $ , we get
$\Rightarrow \lambda = \dfrac{L}{2} $
According to the question, the length of the pipe is $ 4m $ . Therefore substituting $ L = 4m $ above we get
$\Rightarrow \lambda = \dfrac{4}{2} = 2m $ (1)
So the wavelength of the wave is equal to $ 2m $ .
Now, we know that the frequency and the wavelength of a wave are related by the relation
$\Rightarrow \lambda f = v $
So the frequency of the wave is given by
$\Rightarrow f = \dfrac{v}{\lambda } $
According to the question, $ v = 300m/s $ . Also, from (1) we have $ \lambda = 2m $ . Substituting these above we get
$\Rightarrow f = \dfrac{{300}}{2} $
$ \Rightarrow f = 150Hz $
Thus the frequency of the wave is equal to $ 150Hz $ .
Hence, the correct answer is option C.
Note
We need to be clear with the terminology of the organ pipes. An open organ pipe is a pipe which is closed at both the ends. While a closed organ pipe is closed only at one end. It must be noted that at least one end of the organ pipe must be open.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
