NEET Waves — Set 5

Question 1

A steel wire of length 4 m and mass 0.08 kg is under tension. If a transverse wave takes 0.02 s to travel its length, what is the tension?

Accepted Answer

Speed: $ v = \frac{\text{length}}{\text{time}} = \frac{4}{0.02} = 200 \, \text{m/s} $. $ \mu = \frac{0.08}{4} = 0.02 \, \text{kg/m} $. $ v = \sqrt{\frac{T}{\mu}} \Rightarrow 200 = \sqrt{\frac{T}{0.02}} \Rightarrow 200^2 = \frac{T}{0.02} $. $ T = 40000 \times 0.02 = 800 \, \text{N} $.

Question 2

A closed pipe of length 0.3 m has a speed of sound of 330 m/s. What is the frequency of its fifth harmonic?

Accepted Answer

For closed pipe: $ v_n = (n + \frac{1}{2}) \frac{v}{2L} $, $ n = 4 $ for fifth harmonic. $ v_4 = (4 + \frac{1}{2}) \frac{330}{2 \times 0.3} = 4.5 \times \frac{330}{0.6} = 4.5 \times 550 = 2475 \, \text{Hz} $.

Question 3

A pipe open at both ends has a length of 0.57 m and resonates with a source of frequency 900 Hz. What is the harmonic number if the speed of sound is 342 m/s?

Accepted Answer

$ v_n = \frac{n v}{2L} $. $ 900 = \frac{n \times 342}{2 \times 0.57} = \frac{n \times 342}{1.14} $. $ 900 = n \times 300 \Rightarrow n = \frac{900}{300} = 3 $. Third harmonic.

NEET Physics: Waves — Practice Set 5

Q1. A steel wire of length 4 m and mass 0.08 kg is under tension. If a transverse wave takes 0.02 s to travel its length, what is the tension?

Q2. A closed pipe of length 0.3 m has a speed of sound of 330 m/s. What is the frequency of its fifth harmonic?

Q3. A pipe open at both ends has a length of 0.57 m and resonates with a source of frequency 900 Hz. What is the harmonic number if the speed of sound is 342 m/s?

Q4. A transverse wave travels on a string with a speed of 20 m/s and a frequency of 10 Hz. What is its wavelength?

Q5. A stationary wave is given by \( y = 0.05 \sin (\frac{2\pi x}{5}) \cos (100\pi t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the wavelength?

Q6. Which property of a gas affects the speed of longitudinal waves more significantly than its density?

Q7. Which factor primarily determines the pitch of a sound wave as perceived by a listener?

Q8. Which condition is essential for the formation of a standing wave in a medium?

Q9. A string fixed at both ends has a length of 2.5 m and a wave speed of 100 m/s. What is the frequency of its fourth harmonic?

Q10. A wave on a string has an amplitude of 0.06 m and a frequency of 30 Hz. What is the maximum transverse acceleration of a particle?

Q11. A steel rod of length 2 m and density 7800 kg/m³ has a longitudinal wave speed of 5000 m/s. What is its Young’s modulus?

Q12. In a transverse wave, what is the relationship between particle velocity and wave velocity at an antinode of a standing wave?

Q13. A pipe open at both ends has a length of 0.6 m and a wave speed of 300 m/s. What is the difference in frequency between the third and first harmonics?

Q14. Why can’t transverse waves propagate through a liquid medium?

Q15. A sound wave in air has a frequency of 170 Hz and wavelength of 2 m. What is the speed of sound in air?