C.4 Standing waves and resonance

A standing wave is formed in a pipe closed at one end. The third harmonic has a frequency of 400 Hz when the speed of sound is 300 m s⁻¹. What is the length of the pipe?

A.  $\frac{3}{16}$ m

B.  $\frac{9}{16}$ m

C.  $\frac{3}{4}$ m

D.  $\frac{14}{16}$ m

A standing wave is formed in a pipe closed at one end. The third harmonic has a frequency of 400 Hz when the speed of sound is 300 m s⁻¹. What is the length of the pipe?

A.  $\frac{3}{16}$ m

B.  $\frac{9}{16}$ m

C.  $\frac{3}{4}$ m

D.  $\frac{14}{16}$ m

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

In an experiment to determine the speed of sound in air, a tube that is open at the top is filled with water and a vibrating tuning fork is held over the tube as the water is released through a valve.

An increase in intensity in the sound is heard for the first time when the air column length is $x$. The next increase is heard when the air column length is $y$.

Which expressions are approximately correct for the wavelength of the sound?

I. 4$x$

II. 4$y$

III. $\frac{4y}{3}$

A. I and II

B. I and III

C. II and III

D. I, II and III

In an experiment to determine the speed of sound in air, a tube that is open at the top is filled with water and a vibrating tuning fork is held over the tube as the water is released through a valve.

An increase in intensity in the sound is heard for the first time when the air column length is $x$. The next increase is heard when the air column length is $y$.

Which expressions are approximately correct for the wavelength of the sound?

I. 4$x$

II. 4$y$

III. $\frac{4y}{3}$

A. I and II

B. I and III

C. II and III

D. I, II and III

A third-harmonic standing wave of wavelength 0.80 m is set up on a string fixed at both ends. Two points on the wave are separated by a distance of 0.60 m. What is a possible phase difference between the two points on the wave?

A. $\frac{\pi }{4}\text{rad}$

B. $\frac{\pi }{2}\text{rad}$

C. $\pi \text{rad}$

D. $\frac{3\pi }{2}\text{rad}$

A third-harmonic standing wave of wavelength 0.80 m is set up on a string fixed at both ends. Two points on the wave are separated by a distance of 0.60 m. What is a possible phase difference between the two points on the wave?

A. $\frac{\pi }{4}\text{rad}$

B. $\frac{\pi }{2}\text{rad}$

C. $\pi \text{rad}$

D. $\frac{3\pi }{2}\text{rad}$

Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.

Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.

The air in a pipe, open at both ends, vibrates in the second harmonic mode.

What is the phase difference between the motion of a particle at P and the motion of a particle at Q?

A.  $0$

B.  $\frac{\mathrm{\pi }}{2}$

C.  $\mathrm{\pi }$

D.  $2\mathrm{\pi }$

The air in a pipe, open at both ends, vibrates in the second harmonic mode.

What is the phase difference between the motion of a particle at P and the motion of a particle at Q?

A.  $0$

B.  $\frac{\mathrm{\pi }}{2}$

C.  $\mathrm{\pi }$

D.  $2\mathrm{\pi }$

A pipe of length L is closed at one end. Another pipe is open at both ends and has length 2L. What is the lowest common frequency for the standing waves in the pipes?

A. $\frac{\text{speed of sound in air}}{8\text{L}}$

B. $\frac{\text{speed of sound in air}}{4\text{L}}$

C. $\frac{\text{speed of sound in air}}{2\text{L}}$

D. $\frac{\text{speed of sound in air}}{\text{L}}$

A pipe of length L is closed at one end. Another pipe is open at both ends and has length 2L. What is the lowest common frequency for the standing waves in the pipes?

A. $\frac{\text{speed of sound in air}}{8\text{L}}$

B. $\frac{\text{speed of sound in air}}{4\text{L}}$

C. $\frac{\text{speed of sound in air}}{2\text{L}}$

D. $\frac{\text{speed of sound in air}}{\text{L}}$

The string is made to vibrate in its third harmonic. State the distance between consecutive nodes. 

The string is made to vibrate in its third harmonic. State the distance between consecutive nodes. 

The string is made to vibrate in its third harmonic. State the distance between consecutive nodes. 

The tube is raised until the loudness of the sound reaches a maximum for a second time.

Draw, on the following diagram, the position of the nodes in the tube when the second maximum is heard.

The tube is raised until the loudness of the sound reaches a maximum for a second time.

Draw, on the following diagram, the position of the nodes in the tube when the second maximum is heard.

The tube is raised until the loudness of the sound reaches a maximum for a second time.

Draw, on the following diagram, the position of the nodes in the tube when the second maximum is heard.

Between the first and second positions of maximum loudness, the tube is raised through 0.37 m. The speed of sound in the air in the tube is 320 m s⁻¹. Determine the frequency of the sound emitted by the loudspeaker.

Between the first and second positions of maximum loudness, the tube is raised through 0.37 m. The speed of sound in the air in the tube is 320 m s⁻¹. Determine the frequency of the sound emitted by the loudspeaker.

Between the first and second positions of maximum loudness, the tube is raised through 0.37 m. The speed of sound in the air in the tube is 320 m s⁻¹. Determine the frequency of the sound emitted by the loudspeaker.

A standing wave is formed on a string. P and Q are adjacent antinodes on the wave. Three statements are made by a student:

I.   The distance between P and Q is half a wavelength.
II.  P and Q have a phase difference of π rad.
III. Energy is transferred between P and Q.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A standing wave is formed on a string. P and Q are adjacent antinodes on the wave. Three statements are made by a student:

I.   The distance between P and Q is half a wavelength.
II.  P and Q have a phase difference of π rad.
III. Energy is transferred between P and Q.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A standing wave is formed on a rope. The distance between the first and fifth antinode on the standing wave is 60 cm. What is the wavelength of the wave?

A.  12 cm

B.  15 cm

C.  24 cm

D.  30 cm

A standing wave is formed on a rope. The distance between the first and fifth antinode on the standing wave is 60 cm. What is the wavelength of the wave?

A.  12 cm

B.  15 cm

C.  24 cm

D.  30 cm

Adjacent minima are separated by a distance of 0.12 m. Calculate $f$.

Adjacent minima are separated by a distance of 0.12 m. Calculate $f$.

Adjacent minima are separated by a distance of 0.12 m. Calculate $f$.

A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A.  $\frac{(2n-1)V}{2L}$

B.  $\frac{(2n-1)V}{4L}$

C.  $\frac{nV}{2L}$

D.  $\frac{nV}{4L}$

A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A.  $\frac{(2n-1)V}{2L}$

B.  $\frac{(2n-1)V}{4L}$

C.  $\frac{nV}{2L}$

D.  $\frac{nV}{4L}$

A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A.  $\frac{(2n-1)V}{2L}$

B.  $\frac{(2n-1)V}{4L}$

C.  $\frac{nV}{2L}$

D.  $\frac{nV}{4L}$

A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A.  $\frac{(2n-1)V}{2L}$

B.  $\frac{(2n-1)V}{4L}$

C.  $\frac{nV}{2L}$

D.  $\frac{nV}{4L}$

A standing wave with a first harmonic of frequency $f_1$ is formed on a string fixed at both ends.

The frequency of the third harmonic is $f_3$.

What is $\frac{f_1}{f_3}$?

A.  3

B.  $\frac{3}{2}$

C.  $\frac{2}{3}$

D.  $\frac{1}{3}$

A standing wave with a first harmonic of frequency $f_1$ is formed on a string fixed at both ends.

The frequency of the third harmonic is $f_3$.

What is $\frac{f_1}{f_3}$?

A.  3

B.  $\frac{3}{2}$

C.  $\frac{2}{3}$

D.  $\frac{1}{3}$

A standing wave with a first harmonic of frequency $f_1$ is formed on a string fixed at both ends.

The frequency of the third harmonic is $f_3$.

What is $\frac{f_1}{f_3}$?

A.  3

B.  $\frac{3}{2}$

C.  $\frac{2}{3}$

D.  $\frac{1}{3}$

A standing wave with a first harmonic of frequency $f_1$ is formed on a string fixed at both ends.

The frequency of the third harmonic is $f_3$.

What is $\frac{f_1}{f_3}$?

A.  3

B.  $\frac{3}{2}$

C.  $\frac{2}{3}$

D.  $\frac{1}{3}$

A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$.

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$?

A.  400 Hz

B.  200 Hz

C.  100 Hz

D.  50 Hz

A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$.

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$?

A.  400 Hz

B.  200 Hz

C.  100 Hz

D.  50 Hz

A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$.

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$?

A.  400 Hz

B.  200 Hz

C.  100 Hz

D.  50 Hz

A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$.

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$?

A.  400 Hz

B.  200 Hz

C.  100 Hz

D.  50 Hz