Stationary waves

A student carries out an experiment to measure the frequency, f, of the mains electricity supply, using the apparatus shown in the diagram.

The wire passes between the poles of a magnet. It is held in tension by the weight W of the mass hanger. The fixed bridge and the movable bridge are separated by distance L.

Mains frequency current is passed through the wire. The student adjusts the movable bridge until the wire vibrates at its fundamental frequency. The weight W and the length L are recorded. This is repeated for several different weights.

Explain how a stationary wave is formed on the wire.

It can be shown that the fundamental frequency f₀ of a wire of length L under tension W is given by the equation

where is the mass per unit length of the wire, and has a value of 8.0 × 10^–4 kg m^–1 ± 2%.

Suggest why the magnetic flux density, B, of the magnet does not appear in this equation.

Suggest a method to determine the mass per unit length, , of the wire.

The graph shows the results of the experiment.

The student draws a best fit line on the graph. The gradient of the best fit line is 2.81 N^1/2m^–1.

Draw a worst acceptable line on the graph.

Use your worst acceptable line to calculate the percentage uncertainty in the gradient of the best fit line.

gradient = 2.81 ±........ N^1/2m^–1%

Calculate a value for the mains frequency, f, including a percentage uncertainty.

f =........ Hz ±........ %

Evaluate the accuracy of your value for f, given that the true value is 50.0 Hz.

The diagram shows a string stretched between two posts.

The string is plucked and a stationary wave is set up.

What is the phase difference between P and Q?

A 0 rad

D rad

Your answer

A flute is a musical instrument made from a long tube that is open at both ends.

A stationary sound wave in the tube produces a musical note.

The lowest frequency note that a standard flute produces in air is 262 Hz.

The speed of sound in air at a temperature of 20 °C is 340 m s^–1.

Show that a standard flute has an approximate length of 0.65 m.

In an ideal gas, the speed v of sound is given by

where

is a dimensionless constant that depends on the gas

R is the molar gas constant

T is the absolute temperature

M is the molar mass of the gas.

The table below shows values of and M for both air and helium.

Gas		M / g mol–1
Air	1.40	29.0
Helium	1.67	4.00

The kinetic model of an ideal gas assumes that there are a large number of particles in rapid, random motion.

State two further assumptions for the kinetic model of an ideal gas.

A standard flute is placed inside a sealed chamber.

The chamber is filled with helium at a temperature of –10 °C.

Calculate the lowest frequency that the flute could produce inside the chamber.

A graph of displacement s against distance x for a progressive wave at time t = 0 is shown

Determine:

the phase difference in radians between the points on the wave at x = 1.5 cm and x = 2.5 cm

the displacement s at time t = T at x = 1.5 cm, where T is the period of the oscillations of the wave.

A student is doing an experiment to determine the speed of sound in air by producing stationary waves inside a horizontal glass tube.

Fine powder is sprinkled inside the tube. A loudspeaker is placed close to the open end of the tube. The other end of the tube is closed. The loudspeaker is connected to a signal generator producing a frequency of 2.72 kHz. The powder inside the tube forms piles at certain locations inside the tube, see Fig. 16.2.

Suggest why the powder piles up at the nodes within the tube.

Determine the fundamental (minimum) frequency f₀ of the stationary wave that can be formed within this tube.

A stationary sound wave formed in a tube is shown below.

The tube is closed at one end. The length of the tube is 3.5 m. The speed of sound is 340 m s^–1.

What is the frequency of the sound wave?

A 97 Hz

B 120 Hz

C 240 Hz

D 486 Hz

Your answer

The normal frequency range of hearing for young people is from 20 Hz to 20 kHz.

Describe how you can use an oscilloscope, and other additional laboratory equipment, to determine the actual upper limit of the frequency range for a young person.

State one difference and one similarity between the oscillations of a stationary sound wave and a progressive sound wave.

You are provided with a ray-box, a semi-circular block of plastic and other normal laboratory equipment. The outline of the block is shown below.

Describe how you could measure the refractive index n of the block using the critical angle method. Draw on the diagram and label it to make your answer clear.

This question is about a progressive wave and a stationary wave.

Which statement is correct?

A A progressive wave has at least one node.

B All progressive waves are longitudinal.

C All particles oscillating between two adjacent nodes in a stationary wave are in phase.

D The superposition of two waves travelling in the same direction produces a stationary wave.

Your answer

Calculate the frequency f of the transmitted wave.

The electromagnetic wave is caused by electrons oscillating in the transmitter aerial. Each electron oscillates with simple harmonic motion.

Calculate the maximum acceleration a_max of an electron which oscillates with an amplitude of 4.0 × 10^–6 m.

=........ m s^–2 a_max

Suggest why the diode in Fig. 5.1 is necessary for an ammeter to detect a signal at the receiver aerial.

Fig. 17.1 shows the variation with distance of the displacement of a stationary wave at time

The period of the wave is T.

On Fig. 17.1, sketch a graph to show the variation of the displacement at time t =

On Fig. 17.1, show the positions of all the nodes. Label each node N.

A vibrating tuning fork is held above the open end of a long vertical tube. The other end of the tube, which is also open, is immersed in a tank of water. The length L of the air column within the tube is changed by raising or lowering the tube.

The wavelength of sound from the vibrating tuning fork is 150.0 cm.

What length L of air column will not produce a stationary wave within the tube?

A 37.5 cm

B 75.0 cm

C 112.5 cm

D 187.5 cm

Your answer

Stationary waves are produced in a tube closed at one end and open at the other end. The fundamental frequency is 120 Hz.

What is a possible frequency of a harmonic for this tube?

A 60 Hz

B 240 Hz

C 360 Hz

D 480 Hz

Your answer