4.2 Travelling Waves

A signal generator is connected to a loudspeaker and produces an output signal with 6.70 × 10² oscillations per second.

Determine the wavelength, λ, of the sound wave.

The graph shows the change in pressure, Δp, at point P as a function of time, t, as the sound wave passes. 

Deduce the value of t₀.

State the phase of the oscillation at point Q relative to point P and justify your answer.

Suggest and explain one other feature of the Δp-t graph that would be different at point Q in relation to point P. 

Ultrasound is used to measure the depth of oceans, seas and lakes. 

The diagram shows a pulse of ultrasound being emitted from the boat, travelling down to the sea bed and being reflected back to the boat.

Outline the term ultrasound.

A cathode-ray oscilloscope (C.R.O.) is used to trace the ultrasound pulses sent from the boat and the reflected pulses returning to the boat.

The ultrasound travels through water at 1 452 m s⁻¹, and the wavelength of the pulse is 0.023 m.

For the ultrasound pulses: 

The boat moves out to an area where the sea is deeper. 

A boulder falls into a lake and ripples propagate radially outwards. Two boats on the surface of the water are in line with the source and perform the simple harmonic motion, bobbing up and down as the ripples pass by. The boats are separated by a distance of 45 m.

Two observations were recorded; the first ripple took 3.8 s to travel between the boats; the boats are completely out of phase. 

Calculate the speed of the water wave.

Explain why the amplitude of the wave will decrease with increasing distance from the source.

A sound wave in air has a speed of 330 m s^-1. The distance between a rarefaction and compression is 1.3 m for this particular soundwave.

Calculate the time period of the sound wave.

A stone is dropped into a metal bath filled with water, and the sound of it landing is heard by a person in the room.

The sound waves generated by the impact of the stone travels to the person at different speeds through the metal of the bath, the water and the air.

The metal of the bath is 0.5 cm thick, the water is 23 cm deep, and the ears of the person are 160 cm above the base of the bath.

You may use the following values:

Speed of sound in air = 330 m s^-1

Speed of sound in metal = 3000 m s^-1

Speed of sound in water = 1500 m s^-1  

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[3]

The graph shows the displacement y of the particles in air due to the progression of the sound wave x  from the source to the ear.

Positive displacement indicates movement towards the person and negative displacement is away from them.

Annotate on a sketch of the graph the position of at least two compressions and two rarefactions.

The graph shows the variation with time t of the displacement y of a particle in the metal of the bath.

For the longitudinal wave:

(i)    Calculate the frequency of the wave

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(ii)   Determine the speed it is moving at when t = 0.15 s

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 (i)   Outline what is meant by an electromagnetic (EM) wave.

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 (ii)  Compare EM waves to ultrasound waves.

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When doctors want to use medical imaging to observe a foetus in the uterus, ultrasound is used rather than x-rays.

Ultrasound produces images which are less detailed.

Electromagnetic waves can be modelled using a stretched string with a wave passing along it. In the diagram, a wave is travelling to the right. The equilibrium position of the waveform is marked with a dashed line and a point, P is indicated.

The frequency of the wave is 0.5 Hz.

Annotate the diagram as instructed below.

(i)   Starting at point P, identify the wavelength of the wave.

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(ii)   Indicate the motion of point P from the instant until 0.5 s later.

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The string is being oscillated at one end to cause a frequency f of 0.5 Hz and wavelength, λ of 30 cm.

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Ultrasound scanners are used in hospitals to establish the depth of internal organs under the skin. A pulse of ultrasound is emitted from a transducer, which also detects reflections of the pulse from internal organs.

Reflected pulses are displayed on the screen of an oscilloscope.

Explain how the energy is transferred in the ultrasound.

The display shows the appearance of the first pulse, Pulse I on an oscilloscope.

Determine the frequency of the pulse of ultrasound.

The scanner emits ultrasound pulses at regular time intervals. A display of two successive pulses, II and III would show a separation between them.  

The reflection of pulse II must be detected before pulse III is emitted. This means that the equipment has a maximum depth within the body which it can clearly create an image from.

Calculate this maximum depth.

•  Speed of ultrasound in body tissue = 1540 m s^-1
• The time-base is set to 20 μs div^-1.

Calculate the wavelength of an electromagnetic wave with a frequency equal to that of the ultrasound wave.

A common investigation to determine the speed of sound uses two microphones connected to a double-beam oscilloscope.

Outline how this equipment can be used to find the speed of sound.

 (i)         List any additional equipment required

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(ii)         Briefly outline the method

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(iii)       Indicate the measurements to be taken

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You may choose to draw a diagram as part of your answer.

Sketch a graph to show the traces which would be observed on the double-beam oscilloscope at a point where:

(i)   No result would be measured and recorded

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(ii)  A result would be measured and recorded

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The teacher planning the investigation to be set up on lab benches where the furthest distance that could be measured is 2.0 m.

Suggest a sensible range of frequencies for the signal generator.

The students consider how their measurements would be different if they could conduct the experiment under different conditions.

Without further calculation, explain what changes would be made to the frequency range used for an experiment conducted

(i)         underwater

(ii)        in a gas tank filled with Helium