Answer: Option D
Which is a possible displacement-time graph for particle Y?
Category Archives: 12 General Wave Properties
General Wave Properties
Oscillating or Vibrating Object in a Wave Motion
When an object is oscillating or vibrating in a wave motion, the speed of the object varies along the path.
In this video, there are 3 examples of vibrating object.
1) Mass vibrating vertically from a spring
2) Pendulum bob oscillating
3) A particle vibrating up and down on a transverse wave
In general, when the object is at the extreme ends of the oscillation or vibration, it is momentarily at rest. Hence its KE at these points is minimum or 0 J.
And in the middle that is where the object is travelling the fastest, hence the KE is the maximum.
Determine the motion of the particles on transverse wave
Instead of imaging how the particles will move and guess their motion, there is a technique which can help you to determine that.
In addition, when particles are in phase, it means that both particles on the wave have the same velocity and same displacement. It means both have the same speed in the same direction and same distance and direction away from the rest position.
Particles that are out of phase means both are having the same speed but in opposite direction.
Refer to the video below to find out more.
Question 01: 2005/2008 PP P1 Q20/Q18
Question 02: 2018 PP P1 Q24
Graphs of Transverse Wave – E.g. Water waves
Refer to the Graphs of Sound Waves here
Slinky coil guru!
Slinky coil can be used to show transverse or longitudinal wave. But do not quote slinky coil as an example of either wave.
But this guy is really pro with a slinky coil!!
Waves
Slinky Coil – Interesting Tricks and demonstrations of Transverse and Longitudinal Waves
Slink coil is usually used to demonstrate the two types of waves – transverse and longitudinal waves. But remember that when you are asked to state an example of each wave, do not quote slinky coil.
View the videos below to know more about the two types of waves.
2017PurePhyP2Q5 Two points on the rope wave with displacement-time graphs given
In this this question, the displacement-time graphs are given, which are different from displacement-distance graphs.
In the displacement-time graphs of A and B, they show the displacement of that particular point at different timing. E,g, at t = 0s, the A is at the rest position (0 displacement) and at time 0.2 s it is at the maximum displacement. This means A is going up from t = 0 s to 0.2 s.
Solutions:
(a) Amplitude: 1.5 cm
(b)(i) Frequency is the number of complete waves produced in 1 second.
(ii) period T = 0.8s, f = 1/T = 1/0.8 = 1.25 Hz
(c) Closest possible positions of A and B, (refer to the video), is when the
time taken for the wave to move from A to B is T/4 = 0.8/4 = 0.2 s.
speed = distance/time = 38/0.2 = 190 cm/s approx. 200 cm/s
(ii) There are various possibilities in which B can be 38 cm to the right of A. Besides T/4, it can be 1.25T or 2.25 T etc. Hence the speed can be other values.
Refer to the video explanation below
Wavefront
Light and sound wave diagram in different mediums with different density
Light and sound are both waves. So both carry energy from one place to another.
Light, which is part of the electromagnetic spectrum, is a transverse wave, It can travel through a vacuum at speed 3.0 x 108 m/s. As the light travels from an optically less dense medium (air) to an optically denser medium (liquid or glass), the light undergoes refraction and bends towards the normal due to a decrease in speed.
Light: Optically less dense medium to denser medium:Â
– speed decreases
– wavelength shorter
– frequency remains constant
Sound is a longitudinal wave. It requires a medium to pass through and it cannot pass through a vacuum. Opposite to light, as the sound travels from a less dense medium (air) into a denser medium (water or solid), the speed increases.
Sound: Less dense medium to denser medium:
– speed increases
– wavelength longer
– frequency remains constant
Refers to the image below to understand how the waves behave in different mediums.
Click here to revise on the calculation of refractive index for light
Using Slinky Coil to demonstrate Transverse and Longitudinal Waves
Though slinky coil is commonly used to demonstrate transverse and longitudinal waves, you must not quote it as an example for either of the waves.
- Transverse waves are waves in which the direction of the wave is perpendicular to the direction of the vibration of the particles. Examples are light wave, water wave or all the waves in the electromagnetic spectrum (which light is one of the waves.
- Longitudinal waves are waves in which the direction of the wave is parallel to the direction of the vibration of the particles. Example is sound wave.
Transverse Waves (slinky coil)
Longitudinal Waves (slinky coil)
Transverse Waves Animation
Longitudinal Waves Animation
Click here to see the simulations of transverse and longitudinal waves.
Period and Frequency
Waves Summary
Click here to view the simulations transverse and longitudinal waves
Students are confused when they need to visualise what is the direction of the particles the next moment of the wave. There is a simpler way solve such question.
Click here to view another example on graphs
Click here to know more about wavefronts created in a ripple tank.
Waves Summary – Amended
Amendments to the Sound information – added info when sound travels from less dense (air) to denser medium (water or solid)
Wave – Displacement-time graph of a particle on a wave
Solutions: Option C
Consider positive displacement if the particle P is above the undisturbed position, and negative displacement if the particle is below the undisturbed position.
The next instance, the particle P will be moving vertically downwards, i.e. moving nearer to its undisturbed position. So the displacement decreases to zero before it moves below the undisturbed position (negative displacement).
Wavefronts
Waves – Confuse with V, f and lamda?
Transverse Wave – Convert to Displacement-Time Graph
Transverse Wave – Position of x at t = 3s
Wavefront
Wavefront is an imaginary line which joins all identical points (e.g. crests) in phase.
Wavefront can be created in a ripple tank.
The video below shows how horizontal wavefront is created.
The video below shows how other types of wavefronts are produced
General Wave Properties – Rope Wave
As Pie is vibrating the rope up and down as shown, creating a transverse wave.
With only vertical displacement (no forward displacement/force is applied to the rope), the speed of the wave is constant.
Since V = fλ, frequency (f) is inversely proportional to wavelength (λ).
Consider the following questions:
a) If Pie wishes to double the frequency of the wave, how should he move his hands?
He should double the speed in which he moves his hands up and down to double the frequency.
b) When the frequency is doubled, what can you say about the wavelength?
Wavelength will be halved. (recall wavelength is inversely proportional to frequency)
c) If Pie wants the waves to be closer, how should he move his hands?
He should increase the speed in which he moves his hands up and down, hence increasing the frquency.
d) If Pie wants to achieve a frequency of 2 Hz, how should he move his hands in order to achieve that?
He should move his hands down and up 2 times (2 complete waves) in 1 second to achieve frequency of 2 Hz.
e) If Pie wants to have a higher amplitude, how should he moves his hands?
He should increase the vertical displacement of the hands to achieve a higher amplitude.
Transverse Waves and Longitudinal Waves
Transverse waves are waves in which the direction of the wave is perpendicular to thedirection of the vibration.
e.g Light, water, and any waves in the electromagnetic spectrum
Longitudinal waves are waves in which the direction of the wave is parallel to the direction of the vibration.
e.g Sound
Wave equation: V = fλÂ
From the rope videos, with only vertical displacement, speed of wave is constant.
Hence frequency is inversely proportional to wavelength. [f increases, λ decreases, and vice versa]
Transverse Waves and Longitudinal Waves
Transverse waves are waves in which the direction of the wave is perpendicular to thedirection of the vibration.
e.g Light, water, and any waves in the electromagnetic spectrum
Longitudinal waves are waves in which the direction of the wave is parallel to the direction of the vibration.
e.g Sound
Wave equation: V = fλÂ
From the rope videos, with only vertical displacement, speed of wave is constant.
Hence frequency is inversely proportional to wavelength. [f increases, λ decreases, and vice versa]
General Wave Properties – Motion of Particles in Transverse Wave
The diagram below shows a wave on a string with particles P, Q, R, S and T on the wave. The wave is moving in the direction as shown.
a) What can you say about the motion of the particles the next moment?
b) What can you say about the motion of the particles at this instant?
Solutions:
a) P:Â down, Q: up, R:Â up, S: down, T: downb) P:Â at rest, Q: up, R:Â at rest, S: down, T: down
b) Take note of P and Q at crest and trough respectively. Hence at this particular instant, P is at its highest point and R is at its lowest point, hence both momentary at rest.
View video tutorial to learn how to draw the wave in the next moment in order to better visualise.
At one glance, both questions seem to be the same. But in actual fact, they are asking about different thing.
Firstly, you have to know that the wave above is transverse wave (wave in which the direction of the vibration is perpendicular to the direction of wave motion). Hence, particles will only vibrate up and down only.
For (a), the question asks about the motion of particles the next moment. You can consider it as in the coming next few seconds.
For (b), it asks about the motion of particles at this particular time as shown.
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