Home
Class 12
PHYSICS
Consider the propagating sound (with vel...

Consider the propagating sound (with velocity `330 ms^(-1)`) in a pipe of length 1.5 m with one end closed and the other open. The frequency associated with the fundamental mode is

A

11 Hz

B

55 Hz

C

110 Hz

D

165 Hz

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the frequency associated with the fundamental mode of sound in a pipe that is closed at one end and open at the other. Here are the steps to arrive at the solution: ### Step-by-Step Solution: 1. **Understand the Pipe Configuration**: - We have a pipe that is closed at one end and open at the other. In this configuration, the closed end will have a node (point of no displacement), and the open end will have an antinode (point of maximum displacement). 2. **Identify the Length of the Pipe**: - The length of the pipe is given as \( L = 1.5 \, \text{m} \). 3. **Determine the Wavelength for the Fundamental Mode**: - For a pipe closed at one end and open at the other, the fundamental frequency (first harmonic) corresponds to a quarter of the wavelength fitting in the length of the pipe. This means: \[ L = \frac{\lambda}{4} \] - Rearranging this gives: \[ \lambda = 4L = 4 \times 1.5 \, \text{m} = 6 \, \text{m} \] 4. **Use the Wave Velocity to Find Frequency**: - The relationship between wave velocity \( v \), frequency \( f \), and wavelength \( \lambda \) is given by: \[ v = f \lambda \] - We know the velocity of sound \( v = 330 \, \text{m/s} \) and we have calculated \( \lambda = 6 \, \text{m} \). We can rearrange the equation to solve for frequency: \[ f = \frac{v}{\lambda} = \frac{330 \, \text{m/s}}{6 \, \text{m}} = 55 \, \text{Hz} \] 5. **Conclusion**: - The frequency associated with the fundamental mode of the sound in the pipe is \( 55 \, \text{Hz} \). ### Final Answer: The frequency associated with the fundamental mode is \( 55 \, \text{Hz} \).
Promotional Banner

Similar Questions

Explore conceptually related problems

A standing wave propagating with velocity 300ms^(-1) in an open pipe of length 4 m has four nodes. The frequency of the wave is

In an organ pipe of length L open at both ends, the fundamental mode has a frequency (where v is a speed of sound in air)

Show that an organ pipe of length 2l open at both ends has the same fundamental frequency as another pipe of length I closed at one end.

An open end organ pipe is 0.50 m long. If the velocity of sound is 320 ms^(-1) , find the frequency of the fundamental note.

Velocity of sound in air is 320 m/s. For an organ pipe closed at one end of length 2 m the resonating frequency may be

The velocity of sound in air is 340ms^(-1) . A pipe closed at one end has a length of 170 cm. neglecting the end correction, the frquencies at which the pipe can resonate are

The length of a pipe open at both ends is 48 cm and its fundamental frequency is 320 Hz. If the speed of sound be 320 ms^( -1) then determine the diameter of the pipe. If one end of the pipe be closed, then what will be the fundamental frequency?

An open pipe is 85 cm long. If the velocity of sound is 340 ms^(-1) , find the frequency of the fundamental note of the pipe. What would be the length of a closed pipe which produces a fundamental note of the same frequency?

Two narrow cylindrical pipes A and B have the same length. Pipe A is open at both ends and is filled with a monoatomic gas of molar mass M_(A) . Pipe B is open at one end and closed at the other end, and is filled with a diatomic gas of molar mass M_(B) . Both gases are at the same temperature. (a) If the frequency of the second harmonic of the fundamental mode in pipe A is equal to the frequency of the third harmonic of the fundamental mode in pipe B , determine the value of M_(B)//M_(B) . (b) Now the open end of pipe B is also closed (so that the pipe is closed at both ends). Find the ratio of the fundamental frequency in pipe A to that in pipe B .

two pipes have each of length 2 m, one is closed at on end and the other is open at both ends. The speed of sound in air is 340 m/s . The frequency at which both can resonate is ?