NEET Waves — Set 10

Question 1

A wave on a string has an amplitude of 0.04 m and a period of 0.02 s. What is the maximum transverse speed of a particle?

Accepted Answer

$ \omega = \frac{2\pi}{T} = \frac{2\pi}{0.02} = 100\pi \, \text{rad/s} $. Max speed: $ v_{\text{max}} = a \omega = 0.04 \times 100\pi \approx 12.56 \, \text{m/s} $.

Question 2

A transverse wave on a string has a frequency of 50 Hz and a wavelength of 0.8 m. What is the speed of the wave?

Accepted Answer

Speed: $ v = v \lambda = 50 \times 0.8 = 40 \, \text{m/s} $.

Question 3

A pipe closed at one end has a length of 0.28 m and a speed of sound of 336 m/s. What is the frequency of its fourth harmonic?

Accepted Answer

For closed pipe: $ v_n = (n + \frac{1}{2}) \frac{v}{2L} $, $ n = 3 $ for fourth harmonic. $ v_3 = (3 + \frac{1}{2}) \frac{336}{2 \times 0.28} = 3.5 \times \frac{336}{0.56} = 3.5 \times 600 = 2100 \, \text{Hz} $.

NEET Physics: Waves — Practice Set 10

Q1. A wave on a string has an amplitude of 0.04 m and a period of 0.02 s. What is the maximum transverse speed of a particle?

Q2. A transverse wave on a string has a frequency of 50 Hz and a wavelength of 0.8 m. What is the speed of the wave?

Q3. A pipe closed at one end has a length of 0.28 m and a speed of sound of 336 m/s. What is the frequency of its fourth harmonic?

Q4. A longitudinal wave in a medium has a speed of 1400 m/s and a density of 800 kg/m³. What is the bulk modulus of the medium?

Q5. A string of length 2.8 m fixed at both ends has a wave speed of 84 m/s. What is the frequency of its fourth harmonic?

Q6. A longitudinal wave in a medium has a speed of 1600 m/s and a density of 1250 kg/m³. What is the bulk modulus of the medium?

Q7. A wave \( y = 0.07 \sin (20x - 60t) \) reflects at a rigid boundary. What is the equation of the reflected wave?

Q8. Why do beats occur only when the frequency difference between two waves is small?

Q9. A string of length 2.5 m and mass 0.05 kg has a wave speed of 100 m/s. What is the tension in the string?

Q10. A wave has an amplitude of 0.05 m and frequency of 15 Hz. What is the maximum transverse acceleration of a particle?