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A position sensor tracks a component undergoing simple harmonic motion. Its displacement from equilibrium is modelled by
where the phase angle is in radians. The amplitude is the period is and the initial phase angle is
State the phase angle at
Calculate the phase angle at in radians.
Calculate the displacement of the component at
State the increase in phase angle during one complete oscillation, in radians.
A string on a musical instrument is fixed at both ends and vibrates in the mode shown in Figure 1.
State the number of displacement nodes and the number of antinodes shown. Count the fixed ends as nodes.
The string has length and the wave speed on it is For the mode shown, calculate the wavelength and frequency. Give both answers to 3 significant figures.
Compare the oscillation amplitudes at A and B, and state their phase difference.
Sound travels at in a pipe of length The pipe is closed at one end and open at the other. Calculate the wavelength and frequency of the third harmonic. Ignore end correction.
A source emits light with wavelength 600 nm and moves directly away from an observer at Take the speed of light as What is the magnitude of the relative change in wavelength, expressed as a percentage?
Answer: C. For light, the magnitude of the relative wavelength change is approximately Thus
A: converts the fractional change to a percentage using a factor of 10 rather than 100.
B: introduces an erroneous factor of
D: shifts the decimal point one place too far when converting the fraction to a percentage.
Remember: multiply a fractional change by 100 to express it as a percentage.
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