MHT CET · Physics · Waves and Sound
The equation of wave is \(\mathrm{Y}=6 \mathrm{sin}\) \(\left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right)\) where ' \(x\) ' is in \(m\) and ' \(t\) ' in
s. The velocity of the wave is
- A \(200 \mathrm{~m} / \mathrm{s}\)
- B \(300 \mathrm{~m} / \mathrm{s}\)
- C \(400 \mathrm{~m} / \mathrm{s}\)
- D \(600 \mathrm{~m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(D) \(600 \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Given: } y=6 \sin \left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right) \\ & \omega t=12 \pi t \\ & \Rightarrow \frac{2 \pi}{T}=12 \pi\end{aligned}\)
\(\begin{aligned}
\therefore \quad \mathrm{T} & =\frac{1}{6} \\
\Rightarrow \mathrm{n} & =6
\end{aligned}\)
Also given \(\frac{2 \pi}{\lambda}=0.02 \pi\)
\(\therefore \quad \lambda=\frac{2}{0.02}=100\)
From equation: \(\mathrm{v}=\mathrm{n} \lambda\), we get
\(\begin{aligned}
\mathrm{v} & =6 \times 100 \\
& =600 \mathrm{~m} / \mathrm{s}
\end{aligned}\)
\(\begin{aligned}
\therefore \quad \mathrm{T} & =\frac{1}{6} \\
\Rightarrow \mathrm{n} & =6
\end{aligned}\)
Also given \(\frac{2 \pi}{\lambda}=0.02 \pi\)
\(\therefore \quad \lambda=\frac{2}{0.02}=100\)
From equation: \(\mathrm{v}=\mathrm{n} \lambda\), we get
\(\begin{aligned}
\mathrm{v} & =6 \times 100 \\
& =600 \mathrm{~m} / \mathrm{s}
\end{aligned}\)
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
- Two identical capacitors have the same capacitance ' \(C\) '. One of them is charged to potential \(\mathrm{V}_1\) and other to \(\mathrm{V}_2\). The negative ends of capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system isMHT CET 2024 Easy
- For an opaque body coefficient of transmission isMHT CET 2010 Easy
- Two discs A and B each of radius \(r\) and mass \(m\) are attached as shown to form a system. The moment of inertia of this system about an axis perpendicular to the plane of the discs and passing through the center of disc \(\mathrm{A}\) is
MHT CET 2022 Medium - A particle carrying a charge equal to 100 times the charge on an electron is rotating one rotation per second in a circular path of radius 0.8 m . The value of magnetic field produced at the centre will be ( \(\mu_0=\) permeability of vacuum)MHT CET 2024 Hard
- Energy of electron in the second orbit of hydrogen atom is E. The energy of electron ' \(E_3\) ' in the third orbit of helium ( \(\left.\mathrm{He}\right)\) atom will beMHT CET 2021 Easy
- When source of sound moves towards a stationary observer, the apparent frequency heard by himMHT CET 2025 Easy
More PYQs from MHT CET
- If the function \(\mathrm{f}(x)=\left\{\begin{array}{ccc}x+a \sqrt{2} \sin x & \text { if } & 0 \leq x \leq \frac{\pi}{4} \\ 2 x \cot x+\mathrm{b} & \text { if } & \frac{\pi}{4} < x \leq \frac{\pi}{2} \\ a \cos 2 x-\mathrm{bsin} x & \text { if } & \frac{\pi}{2} < x \leq \pi\end{array}\right.\) is continuous in \([0, \pi]\) then \(a-b=\)MHT CET 2025 Medium
- Two rods of same length and material are joined end to end. They transfer heat in 8 second. When they are joined in parallel they transfer same amount of heat in same conditions in timeMHT CET 2021 Medium
- The radius of right circular cylinder increase at the rate \(0.1 \mathrm{~cm} / \mathrm{min}\) and height decreases at the rate of \(0 \cdot 2 \mathrm{~cm} / \mathrm{min}\) The rate of change of volume of the cylinder in \(\mathrm{cm}^3 / \mathrm{min}\), when the radius is \(2 \mathrm{~cm}\) and height is \(3 \mathrm{~cm}\), isMHT CET 2022 Medium
- For \(\mathrm{k}=1,2,3\) the box \(\mathrm{B}_{\mathrm{k}}\) contains k red balls and \((\mathrm{k}+1)\) white balls. Let \(\mathrm{P}\left(\mathrm{B}_1\right)=\frac{1}{2}, \mathrm{P}\left(\mathrm{B}_2\right)=\frac{1}{3}\) and \(\mathrm{P}\left(\mathrm{B}_3\right)=\frac{1}{6}\). A box is selected at random and a ball is drawn from it. If a red ball is drawn from it, then the probability that it comes from box \(B_2\) isMHT CET 2025 Medium
- Two discs of same mass ąnd same thickness (t) are made from two different materials of densities ' \(\mathrm{d}_1\) ' and ' \(\mathrm{d}_2\) ' respectively. The ratio of the moment of inertia \(\mathrm{I}_1\) to \(\mathrm{I}_2\) of two discs about an axis passing through the centre and perpendicular to the plane of disc isMHT CET 2023 Medium
- The value of \(\cos ^{-1}\left(\cos \frac{8 \pi}{3}\right)\) isMHT CET 2020 Easy