Stationary Waves (AQA AS Physics)

Two radio transmitters emit waves at a frequency of 2.5 MHz. A stationary wave is set up between the two transmitters due to the superposition of the radio waves.

What is the minimum distance between two nodes in the stationary wave?

The frequency of the first harmonic of a standing wave on a wire is f. Another wire of the same type, but with triple the length and triple the tension, is used.

What is the resulting frequency of the first harmonic?

A loudspeaker emits a sound wave which is reflected by a metal sheet.

The diagram shows the pattern produced due to superposition of the emitted and reflected waves:

Q, R, S and T are four points on the line through the centre of these waves.

Which of the following statements is correct?

The diagram below shows sound wave produced in a column by a loudspeaker. The speed of sound in air is 330 m s⁻¹.

What is the frequency of the wave?

Which one of the following statements about stationary waves is correct?

A student was investigating the speed of a transverse wave on a stretched spring. They found that by adjusting the tension on the spring, they were able to change the speed.

The wave pattern produced is shown in the diagram the frequency of the oscillator was set to 650 Hz

What needs to be changed to maintain the same wave pattern when the frequency is increased to 750 Hz?

Headphones that have noise reduction can cancel out external noise by producing their own waves.

They are fitted with a microphone that detects the external sound frequency. The loudspeaker then produces a wave with the same frequency but different phase.

What phase difference is required in order to cancel out the external sound?

Each of the diagrams below show three waves; each of the waves have the same amplitude and frequency but have different phases.

The waves are added together to give a resultant wave. In which case would the resultant wave be zero?

A stationary sound wave produced in a tube has a series of nodes. The distance between the first node and the sixth node is 30 cm

What is the wavelength of the wave?

The speed of a wave on a string can be calculated using the formula

v =

Which line, A to D, in the table below gives the correct units for v, T and μ ?

	v	T
A	m s–1	m	Hz
B	m s–2	Nm	m kg–1
C	m	N	Kg m
D	m s–1	N	kg m–1

Two radio transmitters are set up to emit radio waves of frequency 1.12 MHz. A stationary wave is set up between the two transmitters.

What is the distance between two adjacent nodes in the stationary wave?

At the Cornell Nanofabrication Facility, a tiny guitar has been made out of a single crystal of silicon.

The length of the guitar strings is 10 μm. The guitar can be played but the frequency would be inaudible.

The first harmonic is found at 10 MHz frequency. The string has a mass per unit length of 4 × 10^–12 kg m^–1.

Which of the following is the correct value for the tension in the string?

The frequency of the first harmonic emitted by a plucked violin E string is 659.25 Hz. When the violinist plays the note B, they shorten the length of their string with their finger. The speed of the wave on the string is 428 m s^–1.

If the new note has frequency of 987.77 Hz, by approximately what fraction has the string been shortened?

A first harmonic stationary wave of frequency 145 Hz is established on a string with the following set up. This is called a sonometer.

How can the frequency of the first harmonic be doubled?

A stationary wave is set up on a wire using an oscillator.

The frequency of the stationary wave is 66 Hz.

What is the mass per unit length of the wire, μ?

A uniform wire, is oscillated such that it vibrates at the second harmonic as shown.

What is the phase difference between the oscillations of the particles at F and G?

A 1.08 mm diameter steel guitar wire, of length L = 0.69 m, has a tension T = 14.2 N.

The density of steel is 7800 kg m^–3.

What is the fundamental frequency?

A microwave transmitter is used to direct microwaves of frequency 12.5 GHz along a line ST. A metal plate is positioned at right angles to ST with its mid-point on the line, as shown. The metal plate reflects the microwaves, and a stationary wave is formed.

The detector is moved gradually along ST, and its reading alternates between maxima and minima.

Which one of the following statements is not correct?

An experiment is set up to measure the frequency of the first harmonic at different values of length as shown

The results of the experiment are plotted on a graph

Which one of the following expressions cannot be equal to the gradient of the graph?

The frequency of the first harmonic of a standing wave on a wire is f. The length of the wire and tension in the wire are both halved.

What is the frequency of the first harmonic as a result?