Stationary waves

2 main functions of a cathode ray oscilloscope?

a high resistance voltmeter

to measure short time intervals

high resistance voltmeter?

The settings can be changed to measure different voltages. The magnitude of the vertical deflection is used to measure the magnitude of the voltage - according to the settings

to measure short time intervals?

The C.R.O. time base setting tells you the time interval between events that are one division apart on the C.R.O. screen

microphone?

device that converts sound energy to electrical energy

how can you use a CRO to investigate sound?

The microphone creates an e.m.f. and if a c.r.o. is placed across the microphone it will measure the magnitude of the e.m.f.

The greater the vertical deflection on the screen, the greater the e.m.f

the magnitude of the e.m.f depends on..

the loudness of the sound so the voltage indicates the loudness of the sound

how can frequency be calculated on a CRO?

The time base is set so that one or two full cycles of the sound are shown on the screen.

The no of divisions between two crests can then be counted

The time taken between 2 crests reaching the microphone can then be calculated. This will be the periodic time (T)

The frequency can then be calculated by f = 1/T

interference?

When two waves are in the same area at the same

time they interfere with each other.

constructive interference?

If the two waves arrive in phase with each other we say

they interfere constructively

destructive interference?

If two waves arrive totally out of phase with each other

we say they interfere destructively

principle of superposition?

This states that when two or more waves meet at a point, the

resultant displacement at that point is equal to the sum of the

displacements of the individual waves at that point

example of constructive intereference?

When two crests with amplitude A meet at a point the wave

has amplitude 2A at that point

example of destructive interference?

When a crest and a trough with amplitude A meet the wave has amplitude 0 at the point

If a crest has amplitude A and the trough amplitude 2 A then there will

be..

a trough with amplitude A

stationary waves?

Stationary waves are formed when two waves travelling in the same area have the same frequency, wavelength and amplitude and are travelling in opposite directions

nodes?

The points where the resultant displacement is always zero

antinodes?

The points where maximum displacement is reached

the distance between two adjacent nodes/antinodes is equal to..

λ/2

at any point in time...

all the particles between two adjacent nodes are in phase with each other and totally out of phase with the particles between the next set of antinodes

the amplitude of oscillation depends on..

the distance of the particle from the source

PROGRESSIVE VS STATIONARY WAVES : energy transfer?

P: energy is transferred

S: not transferred

PROGRESSIVE VS STATIONARY WAVES : amplitude?

P: all particles have the same amplitude of oscillation, A

S: the amplitude of oscillation of the particles depends on their position and varies from 2A to zero

PROGRESSIVE VS STATIONARY WAVES : phase of motion?

P: adjacent particles are always out of phase with each other, particles that are λ/2 apart are totally out of phase with each other, particles that are λ apart are in phase with each other

S: adjacent particles are always in phase with each other. particles that are λ/2 apart are totally out of phase with each other

what can stationary waves be used to measure?

wavelength of sound

how would you measure the wavelength of sound?

Set up a stationary sound wave use of signal generator connected to a loudspeaker and a reflecting board

Move a microphone along the line between the loudspeaker and the reflecting board

The distance between two points with minimum sound is λ/2

Usually you measure over several nodes to get a more

accurate measurement

Remember if you do 3 nodes it is 2 x λ/2 and if you do 4 nodes it is 3 x λ/2 and if you do 6 nodes it is 5 x λ/2

You can attach the microphone to a C.R.O. and get the

frequency of the sound and hence measure the speed of

sound

the velocity of sound in a string depends on..

the mass per unit length of the string and the tension in the string

how are waves formed in strings/wires

When a taut string is plucked it creates waves on the string. The waves are reflected from the ends of the string.

When the frequency is such that a stationary wave can be created the string the string vibrates at that frequency

the fixed ends of strings are always..

nodes

the fundamental frequency of the wave is such that..

there is a node at each end and a antinode in the middle

the velocity of sound in air depends on..

the density of the air

sound waves in pipes will also create..

stationary waves at particular frequencies

oscillations in air are..

parallel to energy transfer, even though we sometimes represent them as perpendicular

the open end of a pipe is always..

an antinode

the closed end is always..

a node

stationary waves can also be..

set up in water

The velocity of water waves depends on the depth of the water. The deeper the water the faster the wave