4.2 Travelling Waves

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.

(a)        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

(b)       

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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.

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

(d)        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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(a)       

 (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.

(b)     

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.

(c)       

(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.

(d)       

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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.

(a)        Explain how the energy is transferred in the ultrasound.

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

(b)        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.

(c)        Calculate this maximum depth.

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

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

(a)        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.

(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.

(c)        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.

(i)         underwater

(ii)        in a gas tank filled with Helium

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