Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

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

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 pipe of fixed length is closed at one end. What is $\frac{\text{third harmonic frequency of pipe}}{\text{first harmonic frequency of pipe}}$?

A. $\frac{1}{5}$

B. $\frac{1}{3}$

C. 3

D. 5

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Label a position N that is a node of the standing wave.

Two strings of lengths L₁ and L₂ are fixed at both ends. The wavespeed is the same for both strings. They both vibrate at the same frequency. L₁ vibrates at its first harmonic. L₂ vibrates at its third harmonic.

What is $\frac{L_1}{L_2}$?

A.   $\frac{1}{3}$

B.   1

C.   2

D.   3

Outline how the standing wave is formed.

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. $\frac{3\pi }{2}\text{rad}$

The sound wave in air in (c) enters a pipe that is open at both ends. The diagram shows the displacement, at a particular time T, of the standing wave that is set up in the pipe.

On the diagram, at time T, label with the letter C a point in the pipe that is at the centre of a compression.

State the frequency of the wave in air.

Water is draining from a vertical tube that was initially full. A vibrating tuning fork is held near the top of the tube. For two positions of the water surface only, the sound is at its maximum loudness.

The distance between the two positions of maximum loudness is x.

What is the wavelength of the sound emitted by the tuning fork?

A.  $\frac{x}{2}$

B.  x

C.  $\frac{3x}{2}$

D.  2x

Draw on the diagram the standing wave at time $t=\frac{T}{4}$.

Outline how the standing wave is formed.

Sketch, on the diagram, the variation of displacement of the air molecules with distance along the pipe when t = $\frac{3}{4f}$.

The diagram shows a second harmonic standing wave on a string fixed at both ends.

What is the phase difference, in rad, between the particle at X and the particle at Y?

A. 0

B. $\frac{\pi }{4}$

C. $\frac{\pi }{2}$

D. $\frac{3\pi }{4}$

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

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

A string stretched between two fixed points sounds its second harmonic at frequency f.

Which expression, where n is an integer, gives the frequencies of harmonics that have a node at the centre of the string?

A.     $\frac{n+1}{2}f$

B.     nf

C.     2nf

D.     (2n + 1)f

Label a position N that is a node of the standing wave.

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.  $2\mathrm{\pi }$

Determine the wavelength of the wave in air. 

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

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 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 speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

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 particle in the tube has its equilibrium position at the open end of the tube.
State and explain the direction of the velocity of this particle at time $t=\frac{T}{8}$.

Calculate the length of the tube.

A particle in the tube has its equilibrium position at the open end of the tube.
State and explain the direction of the velocity of this particle at time $t=\frac{T}{8}$.

Calculate the length of the tube.

Draw on the diagram the standing wave at time $t=\frac{T}{4}$.