Assertion (A): For a closed organ resonating pipe, the first resonance length is 60 cm. The second resonating length will be 180 cm.
Reason (R): For a particular closed pipe \(n_2 = 3n_1\).
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
For a closed organ pipe, the resonance lengths are in the ratio \(L_1 : L_2 : L_3 = 1 : 3 : 5\). If \(L_1 = 60 text{ cm}\), then \(L_2 = 3 times 60 \text{ cm} = 180 \text{ cm}\). So (A) is true. The resonant frequencies for a closed pipe are \(f_n = (2n-1)f_1\), thus the second resonance (third harmonic) is \(f_2 = 3f_1\). (R) is true and correctly explains (A).
Assertion (A): If two sounds of frequencies 256 Hz and 260 Hz reach our ear simultaneously then we hear a sound of frequency 258 Hz.
Reason (R): We hear a striking variation in the intensity of sound that repeat at a frequency of 4 Hz.
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
When two sound waves of frequencies (f_1) and (f_2) interfere, the perceived average frequency is \((f_1 + f_2)/2 = (256 + 260)/2 = 258 \text{ Hz}\). So (A) is true. The beat frequency is \(|f_1 - f_2| = |256 - 260| = 4 \text{ Hz}\).
So (R) is also true. However, the beat phenomenon does not explain the average perceived frequency.
Assertion (A): When a high pressure pulse of air travelling down an open pipe reaches the other end, turns into a pulse of low pressure pulse travelling up the tube.
Reason (R): Node of pressure means antinode of displacement in case of open 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
At an open end, the pressure must remain atmospheric, establishing a pressure node. An incident high pressure pulse reflects as a low pressure pulse ((pi) phase change) to maintain this. Thus (A) is true. At a pressure node, particles have maximum displacement, which is a displacement antinode. Thus (R) is true and explains the reflection in (A).
Assertion (A): A person hear maximum sound at displacement node.
Reason (R): Pressure change is maximum at displacement node.
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
Our ears perceive sound based on pressure variations. At a displacement node, particles have zero displacement, but pressure variations are maximum (a pressure antinode). Therefore, maximum sound is heard at a displacement node. Both (A) and (R) are true, and (R) provides the direct physical reason for (A).
Assertion (A): In mechanical waves energy transfer takes place because of the coupling through elastic forces between neighbouring oscillating parts of the medium.
Reason (R): Propagation of wave in medium is due to only elastic properties of medium.
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 as mechanical waves transfer energy via the elastic interaction (coupling) of particles. Reason (R) is false because wave propagation in a medium depends on both its elastic properties (like bulk modulus) and its inertial properties (density), not 'only' elastic properties. The speed of a mechanical wave is given by \(v = \sqrt{\frac{\text{Elasticity}}{\text{Inertia}}}\).
Assertion (A): In a hoop revolving with some angular speed \(\omega\) in horizontal plane, transverse wave may appear to be stationary.
Reason (R): Velocity of transverse wave pulse w.r.t. string may be equal and opposite to string velocity.
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. If a transverse wave pulse propagates along the rotating hoop in a direction opposite to the hoop's rotation, and its speed relative to the string is equal to the string's linear speed, the wave appears stationary to a ground observer. Reason (R) provides this exact condition: if \(v_{\text{wave relative to string}} = -v_{\text{string}}\), then the net velocity relative to the lab frame is zero. Both are true and (R) correctly explains (A).
Assertion (A): Transverse mechanical waves cannot be generated within the volume of liquids.
Reason (R): Liquids does not have modulus of rigidity.
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. Transverse waves involve shear deformation perpendicular to the direction of propagation. Reason (R) is true; ideal liquids have a modulus of rigidity (shear modulus) of zero. Since liquids cannot sustain shear stress, they cannot propagate transverse waves internally. Thus, (R) correctly explains (A).
Assertion (A): In longitudinal wave propagation the distance between two consecutive compression is equal to wavelength of wave.
Reason (R): Standing wave is not a wave as it does not transport energy.
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 by definition. Wavelength (\(lambda\)) in a longitudinal wave is the distance between two consecutive compressions or rarefactions. Reason (R) is false; a standing wave is a form of wave resulting from the superposition of two progressive waves. While it does not transfer net energy, it still represents a wave phenomenon with energy oscillation within its segments.
Assertion (A): Sound travels faster in air than in water.
Reason (R): Air is always rarer medium with respect to water medium.
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; sound travels much faster in water (approx. \(1480 \text{ m/s}\)) than in air (approx. \(343 \text{ m/s}\)). Reason (R) is true; air is indeed a rarer (less dense) medium than water. Given that Assertion (A) is false, option 4 is the only choice that fits this condition among the provided options, despite Reason (R) being true.
Assertion (A): Sound waves cannot propagate through vacuum but light waves can.
Reason (R): Sound waves cannot be polarised but light waves can be.
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 because sound waves are mechanical and require a medium, whereas light waves are electromagnetic and can propagate in vacuum.
Reason (R) is true as sound waves are longitudinal and cannot be polarised, while light waves are transverse and can be polarised. However, the ability to polarise is unrelated to propagation through a vacuum.
Thus, (R) is not the correct explanation of (A).