Assertion (A): The pitch of wind instruments rises and that of string instruments falls as an orchestra warms up.
Reason (R): When temperature rises, speed of sound in air increases but speed of wave in a string fixed at both ends decreases.
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 wind instruments, pitch \( f \) is proportional to the speed of sound in air \( v_{\text{air}} propto \sqrt{T_{\text{temp}}} \). As temperature rises, \( v_{\text{air}} \) increases, so pitch rises. For string instruments, \( f propto v_{\text{string}} = \sqrt{T_{\text{tension}}/\mu} \). As temperature rises, the string expands, reducing tension \( T_{\text{tension}} \), so \( v_{\text{string}} \) decreases and pitch falls. Reason R accurately explains this behavior for both cases.
Assertion (A): Sound travels faster on a rainy day than on a dry day.
Reason (R): With increase in humidity pressure increases.
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 \( v = \sqrt{\gamma P/\rho} \). Moist air (humid air) has a lower average molecular mass and thus lower density \( \rho \) than dry air at the same pressure and temperature. A lower density leads to a higher speed of sound. Thus, A is true. Reason R is false; increasing humidity does not necessarily increase total pressure, and the primary factor for faster sound is reduced density.
Assertion (A): Two sound waves of same intensity in a particular medium will have displacement amplitude in ratio of 2:1 if they have frequency in the ratio 1:2.
Reason (R): Two wave of same velocity and amplitude in a particular medium have equal intensity.
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
Intensity of a sound wave is \( I = \frac{1}{2} \rho v \omega^2 A^2 \), where \( \omega = 2\pi f \). If \( I_1 = I_2 \) and the medium is the same (so \( \rho \) and \( v \) are constant), then \( \omega_1^2 A_1^2 = \omega_2^2 A_2^2 \). Given \( f_1 : f_2 = 1 : 2 \), so \( \omega_1 : \omega_2 = 1 : 2 \). This yields \( (1)^2 A_1^2 = (2)^2 A_2^2 \), so \( A_1^2 = 4 A_2^2 \), meaning \( A_1 : A_2 = 2 : 1 \). Thus, A is true. Reason R is false because intensity also depends on frequency (\( \omega \)), so waves with the same velocity and amplitude but different frequencies will have different intensities.
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.
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.
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.
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.
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.
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).