NEET Waves — Set 7

Question 1

A transverse wave on a string has a wavelength of 2 m and a period of 0.04 s. What is the speed of the wave?

Accepted Answer

Frequency: $ v = \frac{1}{T} = \frac{1}{0.04} = 25 \, \text{Hz} $. Speed: $ v = v \lambda = 25 \times 2 = 50 \, \text{m/s} $.

Question 2

A stationary wave is given by $ y = 0.08 \sin (\frac{\pi x}{3}) \cos (60\pi t) $, where $ x $ and $ y $ are in meters and $ t $ in seconds. What is the distance between a node and the next antinode?

Accepted Answer

Form: $ y = A \sin (kx) \cos (\omega t) $, $ k = \frac{\pi}{3} \, \text{rad/m} $. Wavelength: $ \lambda = \frac{2\pi}{k} = \frac{2\pi}{\frac{\pi}{3}} = 6 \, \text{m} $. Distance between node and antinode: $ \frac{\lambda}{4} = \frac{6}{4} = 1.5 \, \text{m} $.

Question 3

A string of length 3 m and mass 0.06 kg has a fundamental frequency of 25 Hz. What is the tension in the string?

Accepted Answer

$ \mu = \frac{0.06}{3} = 0.02 \, \text{kg/m} $. $ v_1 = \frac{v}{2L} \Rightarrow 25 = \frac{v}{2 \times 3} \Rightarrow v = 25 \times 6 = 150 \, \text{m/s} $. $ v = \sqrt{\frac{T}{\mu}} \Rightarrow 150 = \sqrt{\frac{T}{0.02}} \Rightarrow 150^2 = \frac{T}{0.02} $. $ T = 22500 \times 0.02 = 450 \, \text{N} $.

NEET Physics: Waves — Practice Set 7

Q1. A transverse wave on a string has a wavelength of 2 m and a period of 0.04 s. What is the speed of the wave?

Q2. A stationary wave is given by \( y = 0.08 \sin (\frac{\pi x}{3}) \cos (60\pi t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the distance between a node and the next antinode?

Q3. A string of length 3 m and mass 0.06 kg has a fundamental frequency of 25 Hz. What is the tension in the string?

Q4. A wave on a string has an amplitude of 0.03 m and a frequency of 25 Hz. What is the maximum transverse speed of a particle?

Q5. In a longitudinal wave traveling through a gas, what is the relationship between displacement nodes and pressure antinodes?

Q6. In a standing wave formed on a string fixed at both ends, what is the condition for the position of nodes?

Q7. What is the primary source of restoring force for transverse waves on a stretched string?

Q8. Two strings produce beats of 6 Hz. One has a frequency of 384 Hz. When the tension in the second string is decreased, the beat frequency becomes 4 Hz. What was the original frequency of the second string?

Q9. Two waves \( y_1 = 3 \sin (4x - 10t) \) and \( y_2 = 3 \sin (4x - 10t + \pi/2) \) interfere. What is the amplitude of the resultant wave?

Q10. Two strings produce beats of 3 Hz. One has a frequency of 288 Hz. When the tension in the second string is increased, the beat frequency becomes 1 Hz. What was the original frequency of the second string?

Q11. A string of length 1.5 m and mass 0.03 kg has a wave speed of 60 m/s. What is the tension in the string?

Q12. A stationary wave is given by \( y = 0.06 \sin (\frac{\pi x}{4}) \cos (120\pi t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the wavelength?

Q13. Why does a wave reflect with no phase change at a free end?

Q14. Two strings produce beats of 6 Hz. One has a frequency of 300 Hz. When the tension in the second string is decreased, the beat frequency becomes 4 Hz. What was the original frequency of the second string?

Q15. A string of length 0.8 m is fixed at both ends. If the speed of the wave is 40 m/s, what is the frequency of the second harmonic?