NEET Waves — Set 14

Question 1

A string of length 5 m and mass 0.05 kg is under a tension of 80 N. How long does a transverse pulse take to travel its length?

Accepted Answer

Linear mass density: $ \mu = \frac{0.05}{5} = 0.01 \, \text{kg/m} $. Speed: $ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{80}{0.01}} = \sqrt{8000} \approx 89.44 \, \text{m/s} $. Time: $ t = \frac{\text{length}}{v} = \frac{5}{89.44} \approx 0.056 \, \text{s} $.

Question 2

Which condition is necessary for the formation of beats between two waves?

Accepted Answer

Beats require two waves with slightly different frequencies to produce periodic interference, resulting in amplitude modulation. Equal amplitudes or specific wavelengths are not necessary.

Question 3

A pipe closed at one end has a length of 0.5 m and a speed of sound of 340 m/s. What is the frequency of its fundamental mode?

Accepted Answer

Fundamental: $ v_1 = \frac{v}{4L} $. $ v_1 = \frac{340}{4 \times 0.5} = \frac{340}{2} = 170 \, \text{Hz} $.

NEET Physics: Waves — Practice Set 14

Q1. A string of length 5 m and mass 0.05 kg is under a tension of 80 N. How long does a transverse pulse take to travel its length?

Q2. Which condition is necessary for the formation of beats between two waves?

Q3. A pipe closed at one end has a length of 0.5 m and a speed of sound of 340 m/s. What is the frequency of its fundamental mode?

Q4. A pipe open at both ends has a length of 0.3 m and a speed of sound of 330 m/s. What is the frequency of its second harmonic?

Q5. A longitudinal wave travels in a medium with bulk modulus 1.8 × 10⁹ Pa and density 900 kg/m³. What is its speed?

Q6. Which wave type is most likely to propagate fastest in a solid medium?

Q7. A wave on a string has an amplitude of 0.04 m and a period of 0.025 s. What is the maximum transverse speed of a particle?

Q8. A string of length 4 m and mass 0.016 kg is under a tension of 64 N. What is the speed of a transverse wave on the string?

Q9. A string of length 1.8 m and mass 0.036 kg has a fundamental frequency of 50 Hz. What is the tension in the string?

Q10. A wave is described by \( y(x, t) = 0.05 \sin (45x - 90t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the wave speed?