Assertion (A): For a given medium in a wave, particle velocity varies w.r.t. time, while the wave velocity is independent of time.
Reason (R): For propagation of mechanical wave, medium must have the properties of elasticity and inertia.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Particle velocity in a wave is oscillatory and time-dependent, while wave velocity in a homogeneous medium is constant. So, Assertion (A) is true. Mechanical waves require elasticity for restoring force and inertia for propagation. So, Reason (R) is true. However, (R) explains wave propagation conditions, not the difference in velocities.
Assertion (A): Sound is produced due to vibratory motion, but a vibrating pendulum does not produce audible sound.
Reason (R): A vibrating source always produce audible sound.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Sound is produced by vibrations. A vibrating pendulum's frequency is typically below the audible range (infrasound), so it does not produce audible sound. Thus, Assertion (A) is true.
Reason (R) is false because a vibrating source must have a frequency within 20 Hz to 20 kHz to produce audible sound.
Assertion (A): With increase in temperature, the speed of sound in a gas increases.
Reason (R): When temperature increases, the gas molecules move faster.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
The speed of sound in a gas is \(v = \sqrt{\frac{\gamma RT}{M}}\), so it increases with temperature. Thus, Assertion (A) is true. Higher temperature means gas molecules move faster, leading to quicker sound transmission. So, Reason (R) is true and explains (A).
Assertion (A): Sound waves travel faster on a hot summer day than on a cold winter day.
Reason (R): Velocity of sound is directly proportional to the temperature of medium.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Sound speed increases with temperature. A summer day is hotter than a winter day, so sound travels faster. Assertion (A) is true. The velocity of sound in a gas is proportional to the square root of the absolute temperature (\(v \propto \sqrt{T}\)), not directly proportional. So, Reason (R) is false.
Assertion (A): Both arms of a tuning fork vibrate with the same frequency.
Reason (R): The two arms of a tuning fork vibrate in phase.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Both arms of a tuning fork vibrate as a single system, thus at the same frequency. Assertion (A) is true.
For efficient sound production, the arms vibrate 180 degrees out of phase (in opposite directions), not in phase. Therefore, Reason (R) is false.
Assertion (A): Beats are not observed in case of light waves from two independent sources.
Reason (R): The phase difference between two light sources changes randomly.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Stable beats require coherent sources with a constant phase difference. Independent light sources have rapidly and randomly changing phase differences, making stable beats unobservable.
Thus, Assertion (A) is true, and Reason (R) is true and is the correct explanation of (A).
Assertion (A): A tuning fork is in resonance with a closed pipe in fundamental mode, but the same tuning fork cannot be in resonance in fundamental mode with an open pipe of same length.
Reason (R): The same tuning fork will not be in resonance with open pipe of same length due to end correction of pipe.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. For a closed pipe of length \(L\), fundamental frequency is \(v/(4L)\). For an open pipe of same length, it's \(v/(2L)\). These are different, so the same tuning fork cannot resonate in fundamental mode with both. Reason (R) is false; the primary reason is the fundamental frequency difference (\(f_o = 2f_c\)), not solely end correction.
Assertion (A): A vibrating tuning fork sounds louder, when its stem is pressed against a desk top.
Reason (R): When a sound wave is incident on the surface of a desk, it is totally reflected.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true due to forced vibrations and resonance. The desk provides a larger surface area to vibrate, increasing the loudness.
Reason (R) is false because sound waves are not totally reflected; some energy is transmitted to the desk.
Assertion (A): The energy stored by a stationary wave is zero.
Reason (R): When two identical waves travelling in opposite directions superimpose, their whole energy is converted into heat.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is false; a stationary wave stores energy, which oscillates between kinetic and potential forms.
Reason (R) is false; energy is not converted to heat but redistributed to form the stationary wave pattern.
Assertion (A): In \(n^{\text{th}}\) normal mode of a stretched string, there are \(n\) antinodes and \((n+1)\) nodes.
Reason (R): The ends of string are nodes, so the number of nodes is one more than the number of antinodes.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. For a stretched string fixed at both ends, the \(n^{\text{th}}\) normal mode indeed has \(n\) antinodes and \(n+1\) nodes.
Reason (R) is true and correctly explains this: the fixed ends are always nodes, leading to one more node than antinode.