NEET Waves — Set 3

Question 1

What is the significance of the superposition principle in wave phenomena?

Accepted Answer

The superposition principle states that the net displacement of a medium is the algebraic sum of individual wave displacements, enabling phenomena like interference and standing waves.

Question 2

A pipe open at both ends has a length of 0.55 m and a speed of sound of 330 m/s. What is the frequency of its fourth harmonic?

Accepted Answer

For open pipe: $ v_n = \frac{n v}{2L} $. Fourth harmonic ($ n = 4 $): $ v_4 = \frac{4 \times 330}{2 \times 0.55} = \frac{1320}{1.1} = 1200 \, \text{Hz} $.

Question 3

What is the primary factor affecting the speed of sound in a solid rod compared to a gas?

Accepted Answer

In solids, sound speed depends on Young’s modulus ($ v = \sqrt{\frac{Y}{\rho}} $), which measures stiffness and is much higher in solids than the bulk modulus in gases, leading to faster sound propagation.

NEET Physics: Waves — Practice Set 3

Q1. What is the significance of the superposition principle in wave phenomena?

Q2. A pipe open at both ends has a length of 0.55 m and a speed of sound of 330 m/s. What is the frequency of its fourth harmonic?

Q3. What is the primary factor affecting the speed of sound in a solid rod compared to a gas?

Q4. A pipe closed at one end has a length of 0.7 m and resonates at its third harmonic with a speed of sound of 350 m/s. What is the frequency?

Q5. A wave is described by \( y(x, t) = 0.06 \sin (15x - 45t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the frequency of the wave?

Q6. What happens to the phase of a transverse wave when it reflects off a free end of a string?

Q7. A transverse wave travels on a string with tension 250 N and linear mass density 0.05 kg/m. What is the speed of the wave?

Q8. A steel rod of density 7800 kg/m³ has a Young’s modulus of 2 × 10¹¹ Pa. What is the speed of a longitudinal wave in the rod?

Q9. A closed pipe resonates at 425 Hz with a speed of sound of 340 m/s. What is its length?

Q10. A string fixed at both ends has a length of 1.2 m and a wave speed of 72 m/s. What is the frequency of its second harmonic?

Q11. A string of length 1.2 m and mass 0.024 kg has a wave speed of 50 m/s. What is the tension?

Q12. In a progressive wave, what is the key difference between particle displacement and wave propagation direction for a transverse wave?

Q13. A pipe open at both ends has a length of 0.75 m and a speed of sound of 330 m/s. What is the frequency of its second harmonic?

Q14. A wave is described by \( y(x, t) = 0.03 \sin (50x - 200t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is its frequency?

Q15. A stationary wave is given by \( y = 0.02 \sin (\frac{2\pi x}{7}) \cos (140\pi t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the wavelength?