MHT CET · Physics · Waves and Sound
The equation of wave is given by \(y=10 \sin \left(\frac{2 \pi t}{30}+\alpha\right)\). If the displacement is \(5 \mathrm{~cm}\) at \(\mathrm{t}=0\), then the total phase angle at \(\mathrm{t}=7.5 \mathrm{~s}\) will be
- A \(\frac{\pi}{3} \mathrm{rad}\)
- B \(\frac{\pi}{2} \mathrm{rad}\)
- C \(\frac{2 \pi}{5} \mathrm{rad}\)
- D \(\frac{2 \pi}{3} \mathrm{rad}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 \pi}{3} \mathrm{rad}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)\)
At \(\mathrm{t}=0, \mathrm{y}=5 \mathrm{~cm}\)
\(5=10 \sin \alpha\)
\(\alpha=\frac{\pi}{6}\)
At \(\mathrm{t}=7.5\), the total phase
\(\phi=\frac{2 \pi \times 7.5}{30}+\alpha=\frac{\pi}{2}+\frac{\pi}{6}=\frac{2 \pi}{3} \mathrm{rad}\)
At \(\mathrm{t}=0, \mathrm{y}=5 \mathrm{~cm}\)
\(5=10 \sin \alpha\)
\(\alpha=\frac{\pi}{6}\)
At \(\mathrm{t}=7.5\), the total phase
\(\phi=\frac{2 \pi \times 7.5}{30}+\alpha=\frac{\pi}{2}+\frac{\pi}{6}=\frac{2 \pi}{3} \mathrm{rad}\)
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 circular coil and a square coil is prepared from two identical metal wires and a current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that of square coil isMHT CET 2019 Hard
- The amplitude of a particle executing S.H.M. is \(3 \mathrm{~cm}\). The displacement at which its kinetic energy will be \(25 \%\) more than the potential energy isMHT CET 2023 Medium
- A wooden block of mass ' \(m\) ' moves with velocity ' \(v\) ' and collides with another block of mass ' \(4 \mathrm{~m}\) ', which is at rest. After collision the block of mass ' \(m\) ' comes to rest. The coefficient of restitution will beMHT CET 2021 Hard
- An alternating electric field of frequency ' \(v^{\prime}\) is applied across the dees of a cyclotron which is used to accelerate protons of mass 'm'. The radius of the dees is 'R'. The operating magnetic field used in cyclotron is 'B'. The kinetic energy of the proton beam is given byMHT CET 2020 Medium
- Cyclotron is used toMHT CET 2024 Easy
- The graph shows the variation of photocurrent with anode potential for four different radiations. Let \(I_a, I_b, I_c\) and \(I_d\) are intensities and \(f_a, f_b, f_c\) and \(f_d\) be the frequencies for the curves \(a, b, c\) and \(d\) respectively, then
MHT CET 2025 Medium
More PYQs from MHT CET
- The work done during combustion of of ethane, at is (Given , atomic mass )MHT CET 2017 Hard
- The IUPAC name of \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{CH}\left(\mathrm{CH}_{3}\right)_{2}\) isMHT CET 2020 Easy
- If \(B=\left[\begin{array}{ccc}3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3\end{array}\right]\) is the adjoint of \(a\) \(3 \times 3\) matrix \(\mathrm{A}\) and \(|\mathrm{A}|=4\), then \(\alpha\) is equal to8MHT CET 2023 Easy
- Simplify \((p \vee q) \wedge(p \vee \sim q)\)MHT CET 2009 Easy
- With usual notations, if the lengths of the sides of a triangle are \(7 \mathrm{~cm}, 4 \sqrt{3} \mathrm{~cm}\) and \(\sqrt{13} \mathrm{~cm}\), then the measures of the smallest angle isMHT CET 2024 Medium
- Given below are two statements:
Statement I: Back cross is the crossing of \(F _1\) hybrid with one of the two parents from which they were derived.
Statement II: Test cross involves the crossing of \(F _1\) hybrid with its homozygous recessive parent In light of above statements, choose the correct answer from the option given below.MHT CET 2024 Hard