In situation A, an observer moves with a certain velocity towards a stationary source of sound. In situation B, the source moves towards the stationary observer with the same velocity,
Assertion (A): The frequency heard would be the same in both the situations.
Reason (R): The velocity of the source as observed by the observer in both the situations is the same.
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 situation A (observer moving towards stationary source), the observed frequency is \(f_A' = f \frac{v + v_o}{v}\). For situation B (source moving towards stationary observer), the observed frequency is \(f_B' = f \frac{v}{v - v_s}\). If \(v_o = v_s\), then \(f_A' \neq f_B'\). Hence, (A) is false. Classical Doppler effect depends on motion relative to the medium. Although the magnitude of relative velocity between source and observer might be the same, the observed frequencies differ. Thus, (R) is also false as the 'velocity of source as observed by observer' is ambiguous and does not lead to the same frequency due to medium effects. Therefore, both (A) and (R) are false.
Assertion (A): Transverse mechanical waves can propagate in solid, liquid and gas.
Reason (R): Transverse mechanical waves needs rigidity in the medium to propagate.
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
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Transverse mechanical waves require a medium with shear rigidity to propagate in bulk. Solids possess shear rigidity, but bulk liquids and gases do not. Therefore, Assertion (A) is false. Reason (R) is true as rigidity is indeed necessary for transverse wave propagation.
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): 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): 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
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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): 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): Wave velocity is equal to group velocity in a non-dispersive medium.
Reason (R): A non-dispersive medium is one in which the wave velocity is frequency dependent.
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
In a non-dispersive medium, the phase velocity (wave velocity) \(v_p\) is constant, meaning it does not depend on frequency. In this case, group velocity \(v_g\) equals \(v_p\). So (A) is true. Reason (R) is false because a non-dispersive medium has wave velocity independent of frequency.