Wave Velocity and Resonance in Strings and Tubes

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Questions and Answers

What condition must be met for maximum amplitude in oscillation between coupled pendulums?

The mass of the pendulums must be the same.

The pendulums must be fixed at the same point.

The lengths of the pendulums must be different.

The frequency of the driving force must equal the natural frequency of the system. (correct)

How does the velocity of a stationary wave in a string depend on tension and mass per unit length?

Velocity is inversely proportional to tension.

Velocity is directly proportional to the square root of tension and inversely proportional to the square root of mass per unit length. (correct)

Velocity is unaffected by tension and mass per unit length.

Velocity depends solely on the mass per unit length.

Which component of the resonance tube behaves as a node?

The water surface at the closed end. (correct)

The midpoint of the air column.

The open end of the tube.

Anywhere along the air column.

In a resonance situation with a tuning fork and an air column, how is resonance achieved?

By ensuring the length of air column matches the wavelength of the sound. Signup and view all the answers

Which statement about natural frequency is correct?

It is the frequency at which a system oscillates without driving forces. Signup and view all the answers

What happens to the sound amplitude in a resonance tube when the air column reaches specific lengths?

The sound becomes louder at specific lengths due to reinforcement. Signup and view all the answers

What is formed at the open end of a resonance tube?

An antinode. Signup and view all the answers

What effect does varying the water level in a resonance tube have?

It changes the length of the air column and adjusts the resonant frequencies. Signup and view all the answers

What characterizes the formation of resonance in an organ pipe?

A node at the closed end and an antinode at the open end. Signup and view all the answers

How is the wavelength of vibrating air column in a closed organ pipe computed?

$\lambda = \frac{4L}{n}$ for odd harmonics. Signup and view all the answers

What is the relationship between the frequency of a tuning fork and the frequency of the vibrating air column at resonance?

They are equal. Signup and view all the answers

Which harmonic is considered as the first overtone in a closed organ pipe?

Third harmonic. Signup and view all the answers

What is the main difference between harmonics produced in closed and open organ pipes?

Closed organ pipes produce only odd harmonics. Signup and view all the answers

What is the formula for calculating the fundamental frequency of a closed organ pipe?

$f_1 = \frac{v}{4L}$ Signup and view all the answers

What is the significance of the correction 'c' in the resonance equations?

It accounts for the antinode placement just beyond the end of the tube. Signup and view all the answers

What is the characteristic of stationary waves in open organ pipes?

They have an antinode at both ends. Signup and view all the answers

Study Notes

Stationary Wave Velocity in Strings

Velocity of a stationary wave in a string depends on tension and mass per unit length.

Resonance and Resonant Frequency

Several pendulums, suspended from a flexible beam, can oscillate due to coupled vibrations.
The pendulum with a length matching the driving force's frequency oscillates with greater amplitude.
Resonance occurs when the driving frequency matches the natural frequency of the system.
Natural frequency is the oscillation frequency in the absence of an external force.

Resonance Columns

A vibrating tuning fork placed over an open-ended tube partly filled with water can amplify sound.
Sound amplifies when the air column length allows reinforcement of reflected waves.
Resonance occurs at specific air column lengths.
Reinforced waves result from multiple reflections within the tube.

Organ Pipes

Organ pipes produce sound from vibrations in the air column.
Two types: open and closed.
A closed organ pipe has an antinode near the open end and a node at the closed end.
The wavelength of the nth harmonic in a closed organ pipe is 4L/n (n=1, 3, 5...).
The resonant frequencies, fn of a closed organ pipe, are determined by equation fn=nv/4L (n=1, 3, 5...).
Closed pipes produce only odd harmonics.
Open organ pipes have antinodes at both ends.
The wavelength of the nth harmonic in an open pipe is 2L/n (n=1, 2, 3...).
The resonant frequencies, fn of an open pipe, are determined by equation fn=nv/2L (n=1, 2, 3...).
Open pipes produce all harmonics.

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Description

Explore the principles of stationary wave velocity in strings, resonance in pendulums, and the amplification of sound in resonance columns. This quiz covers fundamental concepts like natural frequency and the types of organ pipes. Test your understanding of the relationships between tension, mass, and sound amplification.