The speed of sound in air at 20°C is approximately 343 m/s. The wavelength λ is given by λ = v/f. Thus, λ = 343/440 ≈ 0.78 m.

Wavelength λ is given by the formula λ = v/f. Here, v = 340 m/s and f = 440 Hz. Thus, λ = 340/440 = 0.7727 m, approximately 0.77 m.

The potential difference V = E * d = 200 N/C * 3 m = 600 V.

Using conservation of energy, the potential energy lost equals the rotational kinetic energy gained. The angular velocity ω can be derived as ω = √(2g/L)(1-cosθ).

Using conservation of energy, potential energy at the top = rotational kinetic energy at the bottom. mgh = (1/2)Iω^2. For a rod, I = (1/3)ML^2, h = L/2. Solving gives ω = √(3g/L).

The moment of inertia of a uniform rod about its center is I = 1/12 ML^2.

The angular acceleration α = τ/I = (MgL/2)/(1/3 ML^2) = 3g/2L.

The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.

For a uniformly charged sphere, the electric field outside the sphere behaves as if all the charge were concentrated at the center, thus E = Q/(4πε₀r²).

Convert speed to m/s: 60 km/h = 16.67 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 16.67) / 5 = -3.33 m/s², approximately 3 m/s².

Absolute error is the same as the uncertainty, which is ±0.1 V.

Maximum possible voltage = Measured value + Uncertainty = 12.0 + 0.2 = 12.2 V.

Fractional error = (absolute error / measured value) = 0.3 / 15.0 = 0.02.

The absolute error is given directly as ±5 V.

Relative error = Absolute error / Measured value = 10 / 1000 = 0.01.

Using the formula for density (density = mass/volume), the uncertainty in density can be calculated using the formula for propagation of uncertainty.

Relative error = (Absolute error / Measured value) * 100 = (5 / 200) * 100 = 2.5%

Speed v = f × λ = 50 Hz × 2 m = 100 m/s.

Speed v = f × λ = 50 Hz × 3 m = 150 m/s.

The speed v of a wave is given by v = fλ. Here, v = 600 Hz * 0.5 m = 300 m/s.

The maximum speed v_max is given by v_max = ωA, where ω = 2πf. Thus, ω = 2π(10) = 20π and v_max = 20π(0.5) = 10π ≈ 31.42 m/s.

The amplitude of the wave is the coefficient of the cosine function, which is 0.2 m.

The amplitude of the wave is the coefficient of the cosine function, which is 0.05 m.

The speed of the wave v is given by v = fλ. Here, f = 10 Hz and λ = 2 m (from k = 2π/λ). Thus, v = 10 * 2 = 20 m/s.

The speed of the wave v is given by v = ω/k. Here, ω = 2π(2) = 4π rad/s and k = 2π(0.5) = π rad/m. Thus, v = (4π)/(π) = 4 m/s.

The amplitude is the coefficient of the sine function, which is 0.1 m.

'A' represents the amplitude of the wave, which is the maximum displacement from the equilibrium position.

'k' is the wave number, which is related to the wavelength of the wave.

The wave speed v can be found from the equation v = fλ. Here, f = 4 Hz and λ = 2 m (from k = 2π/λ, k = 1 m⁻¹). Thus, v = 4 Hz * 2 m = 8 m/s.

The speed of the wave v is given by v = fλ. Here, f = 2 Hz and λ = 1 m (from the wave equation). Thus, v = 2 * 1 = 2 m/s.