Assertion (A): When a wave enters from one medium to another, its frequency is not changed.
Reason (R): Speed of a wave in a medium is property of the source.
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
The frequency of a wave is determined by the source that generates it and remains constant as the wave propagates from one medium to another. The speed of a wave, however, is a characteristic property of the medium it is traveling through, not the source. Thus, Assertion A is true, but Reason R is false.
Assertion (A): Two waves moving in a uniform string having uniform tension cannot have different velocities.
Reason (R): Elastic and inertial properties of string are same for all waves in same string. Moreover, velocity of wave in a string depends on its elastic and inertial properties only.
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
The speed of a transverse wave on a string is given by \( v = \sqrt{T/\mu} \), where \( T \) is the tension (elastic property) and \( \mu \) is the linear mass density (inertial property). If the string is uniform (constant \( \mu \)) and has uniform tension (constant \( T \)), then \( v \) must be constant for all waves propagating on it. Both A and R are true, and R correctly explains A.
Assertion (A): Every small part of string does SHM in sinusoidal travelling wave.
Reason (R): In this small segment of string total energy is conserved.
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 sinusoidal traveling wave, each particle of the string oscillates in simple harmonic motion (SHM) perpendicular to the direction of wave propagation. So, Assertion A is true. However, for a *traveling* wave, energy is continuously transmitted along the string. Therefore, the total energy within a small segment of the string is *not* conserved, as energy flows into and out of the segment. Reason R is false.
Assertion (A): In a sinusoidal travelling wave on a string potential energy of deformation of string element at extreme position is maximum.
Reason (R): The particles in sinusoidal travelling wave perform SHM.
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 wave, potential energy is stored due to deformation (strain). At extreme positions (maximum displacement), the deformation is maximum, leading to maximum potential energy. So (A) is true.
Particles in a transverse wave undergo simple harmonic motion. So (R) is true. However, (R) does not explain why potential energy is maximum at extreme positions; it's a general characteristic of the particle motion. Therefore, (R) is not the correct explanation of (A).
Assertion (A): \(Y = 2A sin kx cos \omega t\) refers to a travelling wave along -ve x-direction.
Reason (R): When a continuous travelling wave interacts with its reflection from a rigid support, forms a standing wave.
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
The equation \(Y = 2A sin kx cos \omega t\) represents a standing wave, not a travelling wave. Thus (A) is false. When a travelling wave reflects from a boundary and superposes with the incident wave, a standing wave is formed. Thus (R) is true. Since (A) is false and (R) is true, none of the standard options (A true, R true; A true, R false; A false, R true; A false, R false) perfectly matches. However, given the provided options, and (A) being false, option (4) is selected as it states (A) is false, despite (R) being true.
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
View Answer
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
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).