Page 193 - Physics Coursebook 2015 (A level)

Chapter 13: Waves
WORKED EXAMPLE
1 Figure 13.7 shows the trace on an oscilloscope screen when sound waves are detected by a microphone. The time-base is set at 1 ms div−1. Determine the frequency of the sound waves.
Longitudinal and transverse waves
There are two distinct types of wave, longitudinal and transverse. Both can be demonstrated using a slinky spring lying along a bench.
Push the end of the spring back and forth; the segments of the spring become compressed and then stretched out, along the length of the spring. Wave pulses run along the spring. These are longitudinal waves.
Waggle the end of the slinky spring from side to side. The segments of the spring move from side to side as the wave travels along the spring. These are transverse waves.
So the distinction between longitudinal and transverse waves is as follows:
■■ In longitudinal waves, the particles of the medium vibrate parallel to the direction of the wave velocity.
■■ In transverse waves, the particles of the medium vibrate at right angles to the direction of the wave velocity.
Sound waves are an example of a longitudinal wave. Light and all other electromagnetic waves are transverse waves. Waves in water are quite complex. Particles of the water may move both up and down and from side to side as a water wave travels through the water. You can investigate water waves in a ripple tank. There is more about water waves in Table 13.1 (page 183) and in Chapter 14.
Representing waves
Figure 13.8 shows how we can represent longitudinal
and transverse waves. The longitudinal wave shows how the material through which it is travelling is alternately compressed and expanded. This gives rise to high and low pressure regions, respectively.
Figure 13.7 A c.r.o. trace – what is the frequency of these waves?
Step1 Determinetheperiodofthewavesonthe screen, in scale divisions. From Figure 13.7, you can see that one complete wave occupies three scale divisions (div).
period T = 3.0 div
Step2 Determinethetimeintervalrepresentedby each scale division. The time-base control is set at 1 ms div−1, so:
scale factor = 1 ms div−1
Step3 Converttheperiodindivisionstoms: period T = 3.0div × 1msdiv−1
=3.0ms=3.0×10−3s
Hint: Notice how div and div−1 cancel out.
Step4 Calculatethefrequencyfromtheperiod:
frequencyf=1= 1 −3=333Hz T 3.0×10
So the wave frequency is approximately 330 Hz.
QUESTION
2 When a sound wave is displayed on a c.r.o. screen, two complete waves occupy five scale divisions. The calibrated time-base is set on 0.005 s per division. Determine the frequency of the waves.
a
b
λ
λ
rarefaction compression
Distance
Distance
+ –
A
A
Figure 13.8 a Longitudinal waves and b transverse waves. A = amplitude, λ = wavelength.
181
Displacement