Grade 11 : Physics - Waves (Set 1)

Explanation: Frequency $f$ is the reciprocal of the period $T$:
$$f = \frac{1}{T} = \frac{1}{0.02} = 50\text{ Hz}$$

Explanation: Wave speed $v$ is calculated using $v = f \lambda$:
$$v = 200 \times 1.7 = 340\text{ m/s}$$

Explanation: Sound waves in air are longitudinal mechanical waves because air particles vibrate parallel to the direction of wave energy propagation.

Explanation: Wavelength ($\lambda$) is defined as the spatial distance between two consecutive crests or trough points in phase.

Explanation: Time period ($T$) represents the duration required for one complete oscillation cycle of a wave particle.

Explanation: Amplitude ($A$) is the maximum displacement magnitude of an oscillating particle from its central rest position.

Explanation: Sound is a mechanical wave that requires a material medium. In a vacuum with no particles, sound cannot travel, so its speed is 0 m/s.

Explanation: Light waves consist of perpendicular electric and magnetic field oscillations perpendicular to wave propagation, making them transverse electromagnetic waves.

Explanation: Wave speed on a string is given by:
$$v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{100}{0.01}} = \sqrt{10000} = 100\text{ m/s}$$

Explanation: Pitch is the sensory perception corresponding directly to fundamental frequency; higher frequency corresponds to higher pitch.

Explanation: Loudness correlates with sound energy, which is proportional to the square of the wave amplitude.

Explanation: Phase difference $\Delta \phi = \frac{2\pi}{\lambda} \cdot \Delta x = \frac{2\pi}{\lambda} \cdot \frac{\lambda}{2} = \pi\text{ rad}$.

Explanation: For a pipe open at both ends, the fundamental frequency is:
$$f_1 = \frac{v}{2L} = \frac{340}{2 \times 0.85} = \frac{340}{1.7} = 200\text{ Hz}$$

Explanation: Closed pipes have a node at the closed end and an antinode at the open end, supporting frequencies $f_n = (2n-1)\frac{v}{4L}$, producing only odd harmonics.

Explanation: By the Doppler effect, motion of the source toward an observer compresses wavefronts, increasing observed frequency (higher pitch).

Explanation: The principle of superposition states that the overall displacement is the vector sum of individual wave displacements at that point.

Explanation: Beat frequency equals the absolute difference of two frequencies:
$$f_{\text{beat}} = |f_1 - f_2| = |260 - 256| = 4\text{ Hz}$$

Explanation: Nodes occur at half-wavelength intervals in a standing wave; hence distance between consecutive nodes is $\lambda/2$.

Explanation: Speed of sound in ideal gas is $v = \sqrt{\frac{\gamma R T}{M}}$, which directly implies $v \propto \sqrt{T}$.

Explanation: The angular wave number $k$ measures spatial phase per distance unit, defined as $k = \frac{2\pi}{\lambda}$.