NEET Waves — Set 18

Question 1

Two waves $ y_1 = 5 \sin (7x - 14t) $ and $ y_2 = 5 \sin (7x - 14t + \frac{\pi}{2}) $ interfere. What is the amplitude of the resultant wave?

Accepted Answer

Amplitude: $ A = 2a \cos \frac{\phi}{2} $, $ a = 5 \, \text{m} $, $ \phi = \frac{\pi}{2} $. $ A = 2 \times 5 \cos \frac{\pi}{4} = 10 \times \frac{1}{\sqrt{2}} \approx 7.07 \, \text{m} $.

Question 2

A transverse wave on a string has a speed of 12 m/s and a frequency of 8 Hz. What is its wavelength?

Accepted Answer

Speed: $ v = v \lambda $. Wavelength: $ \lambda = \frac{v}{v} = \frac{12}{8} = 1.5 \, \text{m} $.

Question 3

Which factor directly governs the formation of nodes and antinodes in a standing wave?

Accepted Answer

The boundary conditions (e.g., fixed or free ends) determine where nodes (zero displacement) and antinodes (maximum displacement) occur by enforcing specific wave patterns.

NEET Physics: Waves — Practice Set 18

Q1. Two waves \( y_1 = 5 \sin (7x - 14t) \) and \( y_2 = 5 \sin (7x - 14t + \frac{\pi}{2}) \) interfere. What is the amplitude of the resultant wave?

Q2. A transverse wave on a string has a speed of 12 m/s and a frequency of 8 Hz. What is its wavelength?

Q3. Which factor directly governs the formation of nodes and antinodes in a standing wave?

Q4. A stationary wave on a string fixed at both ends has a frequency of 120 Hz and a wave speed of 48 m/s. What is the length of the string?

Q5. Which factor explains why a transverse wave’s speed is independent of its frequency in a uniform string?

Q6. A pipe open at both ends has a length of 0.4 m and a speed of sound of 320 m/s. What is the frequency of its fourth harmonic?

Q7. What happens to the speed of a longitudinal wave in a gas if the pressure is increased while temperature remains constant?

Q8. A wave is described by \( y(x, t) = 0.02 \sin (50x - 100t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the period of the wave?

Q9. A wave on a string has an amplitude of 0.015 m and a frequency of 40 Hz. What is the maximum transverse speed of a particle?

Q10. A transverse wave on a string has a tension of 144 N and a linear mass density of 0.016 kg/m. What is the wavelength if the frequency is 15 Hz?