Question 1

A guitar string is fingered so that its vibrating length is halved compared to its original length. If the speed of the wave on the string remains unchanged, how does the fundamental frequency change?

Accepted Answer

It is doubled.

Question 2

Which of the following best describes the difference between a node and an antinode in a standing wave?

Accepted Answer

A node is a point of zero displacement, while an antinode is a point of maximum displacement.

Question 3

A tube open at both ends has a length $$L. $$What is the wavelength of the fundamental mode?

Accepted Answer

$$\$$lambda_1$$ = 2L$$

Question 4

The speed of sound in air at $$20^\circC is $$approximately:

Accepted Answer

$$343\ \mathrm{m/s}$$

Question 5

A flute can be modeled as a tube open at both ends. If the tube is $$0.85\ \mathrm{m}$$ long and the speed of sound is $$340\ \mathrm{m/s}$$, what is the fundamental frequency?

Accepted Answer

$$200\ \mathrm{Hz}$$

Question 6

Which equation correctly relates the speed of a wave ($$v$$), its frequency ($$f$$), and its wavelength ($$\lambda$$)?

Accepted Answer

$$v = f \lambda$$

Question 7

A tube closed at one end and open at the other has a length $$L. $$What is the wavelength of its fundamental mode?

Accepted Answer

$$\$$lambda_1$$ = 4L$$

Question 8

Which of the following statements about the harmonic series of a tube closed at one end and open at the other is correct?

Accepted Answer

It contains only odd harmonics.

Question 9

A string fixed at both ends has a length $$L$$ and wave speed $$v. $$What is the frequency of the third harmonic?

Accepted Answer

$$f_3 = 3v / 2L$

Question 10

If the tension in a guitar string is quadrupled, how does the speed of the wave on the string change?

Accepted Answer

It doubles.

Question 11

Which of the following best describes the superposition principle for waves?

Accepted Answer

The displacement at a point is the sum of the displacements of all waves present.

Question 12

A sound wave in air is classified as which type of wave?

Accepted Answer

Longitudinal wave

Question 13

A tube closed at one end and open at the other is $$0.33\ \mathrm{m}$$ long. If the speed of sound is $$340\ \mathrm{m/s}$$, what is the fundamental frequency?

Accepted Answer

$$256\ \mathrm{Hz}$$

Question 14

Which of the following is true about air as a medium for sound waves?

Accepted Answer

Air is a non-dispersive medium; all frequencies travel at the same speed.

Question 15

A string fixed at both ends has a length $$L$$ and mass per unit length $$\mu. If $$the tension is $$F_T$$, what is the speed of the wave on the string?

Accepted Answer

$$v = \sqrt{F_T / \mu}$$

Question 16

Which of the following boundary conditions applies to a tube open at both ends?

Accepted Answer

Antinode at each end

Question 17

A wave pulse reflects from a fixed end. What happens to the pulse?

Accepted Answer

It reflects inverted.

Question 18

For a tube closed at one end and open at the other, which mode numbers $$m$$ are allowed for standing waves?

Accepted Answer

$$m = 1, 3, 5, ...$$

Question 19

A musician tunes a string by increasing its tension. What effect does this have on the pitch (frequency) of the note produced?

Accepted Answer

The pitch increases.

Question 20

Which of the following is the correct formula for the fundamental frequency of a string fixed at both ends?

Accepted Answer

$$f_1 = v / 2L$

Waves and Sound: Properties, Superposition, Standing Waves, and Applications

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