Waves

Practice Questions:

Question 11: easy

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.

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Question 12: easy

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.

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Question 13: easy

Assertion (A): Sound produced by an open organ pipe has good quality than sound produced by a closed organ pipe.

Reason (R): In OOP both even & odd harmonics are present.

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 sound quality of an instrument depends on the number and intensity of overtones present. Because open organ pipes produce a full series of both even and odd harmonics, they generate a richer, higher-quality sound compared to closed pipes, which only produce odd harmonics. Therefore, both (A) and (R) are true, but (R) describes the richness of the open pipe rather than serving as the direct reason for the comparison.

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Question 14: easy

Assertion (A): The fundamental frequency of an open organ pipe increases as the temperature is increased.

Reason (R): As the temperature increases, the velocity of sound increases more rapidly than length of the 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

The fundamental frequency of an open organ pipe is \(f = \frac{v}{2L}\). Velocity of sound \(v\) increases with temperature as \(v \propto \sqrt{T}\). While the pipe's length \(L\) also increases with temperature, the increase in \(v\) is proportionally greater than \(L\). Thus, \(f\) increases. Both A and R are true, and R correctly explains A.

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Question 15: easy

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.

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Question 16: easy

Assertion (A): When there is no relative velocity between source and observer then observed frequency is same as emitted.

Reason (R): Velocity of sound is zero when there is no relative velocity between source and observer.

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

According to the Doppler effect, the observed frequency matches the emitted frequency only when there is no relative motion between the source and observer. So, Assertion (A) is true. The velocity of sound is a property of the medium and is non-zero in an ideal medium, irrespective of relative motion between source and observer. So, Reason (R) is false. Thus, (A) is true but (R) is false.

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Question 17: easy

Assertion (A): Speed of longitudinal wave in solid and liquid is higher than gases.

Reason (R): Modulus of elasticity is more for solids as compared to liquid & gas.

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 longitudinal waves is given by \(v = \sqrt{\frac{B}{\rho}}\), where \(B\) is the bulk modulus. Solids and liquids have significantly higher bulk moduli compared to gases. Thus, longitudinal waves travel faster in solids and liquids. Both assertion and reason are true, and the reason correctly explains the assertion.

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Question 18: easy

Assertion (A): The velocity of sound decreases with increase in humidity.

Reason (R): Velocity of sound does not depend on 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

The velocity of sound increases with humidity because humid air is less dense than dry air. So, Assertion (A) is false. The velocity of sound absolutely depends on the properties of the medium (density, elasticity). So, Reason (R) is also false. Both (A) and (R) are false.

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Question 19: easy

Assertion (A): The change in air pressure, effect the speed of sound at constant temperature.

Reason (R): The speed of sound in a gas is directly proportional to pressure.

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 sound in a gas is \(v = \sqrt{\frac{\gamma RT}{M}}\). At constant temperature (\(T\)), the velocity is independent of pressure. So, Assertion (A) is false. Also, the speed of sound is not directly proportional to pressure. So, Reason (R) is false. Both (A) and (R) are false.

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Question 20: easy

Assertion (A): A (80 \text{ dB}) sound has twice the intensity of a \(40 \text{ dB}\) sound.

Reason (R): Loudness of a sound of a certain intensity (‘I’) is defined as \(L = 10 log_{10} left(frac{I}{I_0}right)\).

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. An 80 dB sound has an intensity \(10^4\) times greater than a \(40 \text{ dB}\) sound, not twice. Reason (R) is true as it correctly defines loudness in decibels.

Since (A) is false and (R) is true, and the option for 'A is false, R is true' is not provided, option (4) is selected as it states (A) is false.

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