KCET · Physics · Waves and Sound
The equation of a wave is given by \(y=10 \sin \left(\frac{2 \pi}{45} t+\alpha\right)\). If the displacement is \(5 \mathrm{~cm}\) at \(t=0\), then the total phase at \(t=7.5 \mathrm{~s}\) is
- A \(\frac{\pi}{3}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{6}\)
- D \(\pi\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(y=10 \sin \left[\frac{2 \pi}{45} t+\alpha\right]\)
\(y=5 \mathrm{~cm}\) at \(t=0\)
\(\therefore \quad 5=10(\sin \alpha)\)
or
\(\sin \alpha=\frac{1}{2}\)
or
\(\alpha=\frac{\pi}{6}\)
Again if \(t=7.5 \mathrm{~s}\)
Then total phase \(=\frac{2 \pi}{45} \times \frac{15}{2}+\frac{\pi}{6}\)
\(=\frac{\pi}{3}+\frac{\pi}{6}\)
\(=\frac{2 \pi+\pi}{6}=\frac{3 \pi}{6}=\frac{\pi}{2}\)
\(y=5 \mathrm{~cm}\) at \(t=0\)
\(\therefore \quad 5=10(\sin \alpha)\)
or
\(\sin \alpha=\frac{1}{2}\)
or
\(\alpha=\frac{\pi}{6}\)
Again if \(t=7.5 \mathrm{~s}\)
Then total phase \(=\frac{2 \pi}{45} \times \frac{15}{2}+\frac{\pi}{6}\)
\(=\frac{\pi}{3}+\frac{\pi}{6}\)
\(=\frac{2 \pi+\pi}{6}=\frac{3 \pi}{6}=\frac{\pi}{2}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A nucleus \({ }_{Z} X^{A}\) emits an \(\alpha\)-particle with velocity \(v\). The recoil speed of the daughter nucleus isKCET 2013 Medium
- In this circuit, when certain current flows, the heat produced in \(5 \Omega\) is \(4.05 \mathrm{~J}\) in a time t. The heat produced in \(2 \Omega\) coil in the same time interval is
KCET 2012 Easy - In a two slit experiment with monochromatic light fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by \(5 \times 10^{-2} \mathrm{~m}\) towards the slits, the change in fringe width is \(3 \times 10^{-5} \mathrm{~m}\). If separation between the slits is \(10^{-3} \mathrm{~m}\), the wavelength of light used isKCET 2008 Medium
- A Carnot's engine operates with source at \(127^{\circ} \mathrm{C}\) and sink at \(27^{\circ} \mathrm{C}\). If the source supplies \(40 \mathrm{~kJ}\) of heat energy, the work done by the engine isKCET 2007 Easy
- If the scattering intensity of a liquid is 8 units at a wavelength of \(500 \mathrm{~nm}\), then the scattering intensity at a wavelength of \(400 \mathrm{~nm}\) will be approximatelyKCET 2011 Hard
- A particle shows distance - time curve as shown in the figure. the maximum instantaneous velocity of the particle is around the point
KCET 2018 Easy
More PYQs from KCET
- The mean and standard deviation of \(100\) items are \(50\) and \(4\), respectively then the sum of all squares of the items isKCET 2026 Easy
- \(\tan^{-1}\left(\dfrac{1}{1 + 1 \cdot 2}\right) + \tan^{-1}\left(\dfrac{1}{1 + 2 \cdot 3}\right) + \ldots + \tan^{-1}\left(\dfrac{1}{1 + n(n+1)}\right) = \)KCET 2026 Medium
- A jet plane of wing span \( 20 \mathrm{~m} \) is travelling towards west at a speed of
\( 400 \mathrm{~ms}^{-1} \). If the earth's total magnetic field is \( 4 \times 10^{-4} \mathrm{~T} \) and the dip angle is \( 30^{\circ} \), at that
place, the voltage difference developed across the ends of the wing isKCET 2017 Easy - Number of stereoisomers exhibited by \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\)isKCET 2020 Easy
- Which of the following compound on heating gives \(\mathrm{N}_{2} \mathrm{O}\) ?KCET 2021 Medium
- A solution of \( 1.25 \mathrm{~g} \) of ' \( \mathrm{P} \) ' in \( 50 \mathrm{~g} \) of water lowers freezing point by \( 0.3{ }^{\circ} \mathrm{C} \). Molar mass of ' \( \mathrm{P} \) ' is
94. \( K_{\mathrm{f}(\text { water })}=1.86 \mathrm{Kg} \mathrm{mol}^{-1} \). The degree of association of ' \( \mathrm{P} \) ' in water isKCET 2014 Easy