Unit 14: Waves , Sound , and Physical Optics
Weightage : 15–18%
The graph below was produced by a microphone in front of a tuning fork. It shows the voltage produced from the microphone as a function of time.
The frequency of the tuning fork is approximately
Correct Answer: \( \boxed{\mathrm{D}} \)
The frequency of a periodic wave is given by
\( \displaystyle f=\frac{1}{T}=\frac{\text{number of cycles}}{\text{time}}. \)
From the graph, approximately 5 complete cycles occur in \(0.020\,\mathrm{s}\).
Therefore,
\( \displaystyle f=\frac{5}{0.020\,\mathrm{s}}=250\,\mathrm{Hz}. \)
Equivalently, the period is about \(T=0.004\,\mathrm{s}\), and
\( \displaystyle f=\frac{1}{0.004\,\mathrm{s}}=250\,\mathrm{Hz}. \)
Therefore, the correct answer is (D).
The figure above shows a transverse wave traveling to the right at a particular instant of time. The period of the wave is \(0.2\,\mathrm{s}\).
What is the amplitude of the wave?
Correct Answer: \( \boxed{\mathrm{A}} \)
The amplitude of a wave is the maximum displacement of a point on the wave from its equilibrium position.
From the diagram, the maximum vertical displacement from the equilibrium line to the crest is
\( \displaystyle A=4\,\mathrm{cm}. \)
The labeled horizontal distance of \(5\,\mathrm{cm}\) is related to the wavelength and does not represent the amplitude.
The given period of \(0.2\,\mathrm{s}\) is not needed to determine the amplitude.
Therefore, the correct answer is (A).
Two tuning forks are struck at the same time. A beat frequency of \(12\,\mathrm{Hz}\) is observed. If one tuning fork has a frequency of \(384\,\mathrm{Hz}\), what could be the frequency of the second tuning fork?
Correct Answer: \( \boxed{\mathrm{B}} \)
The beat frequency is equal to the absolute difference between the two frequencies:
\( f_{\mathrm{beat}}=\left|f_1-f_2\right| \)
Given
\( f_{\mathrm{beat}}=12\,\mathrm{Hz} \) and \( f_1=384\,\mathrm{Hz} \),
the second tuning fork must have a frequency of
\( 384\pm12=372\,\mathrm{Hz} \) or \(396\,\mathrm{Hz} \).
Of the choices given, only \(372\,\mathrm{Hz}\) satisfies this condition.
Therefore, the correct answer is (B).
