The general wave equation for a sound wave is \( y = A \cos(kx - \omega t) \),
where: - \( A \) is the amplitude, - \( k \) is the wave number, and - \( \omega \) is the angular frequency.
The wave velocity \( v \) is given by the formula: \[ v = \frac{\omega}{k}. \]
Thus, the correct answer is option (1).
Two resistances of 100Ω and 200Ω are connected in series with a battery of 4V and negligible internal resistance. A voltmeter is used to measure voltage across the 100Ω resistance, which gives a reading of 1V. The resistance of the voltmeter must be _____ Ω.
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32