NEET Waves — Set 15

Question 1

A pipe open at both ends has a length of 0.85 m and a speed of sound of 340 m/s. What is the frequency of its first harmonic?

Accepted Answer

For open pipe: $ v_n = \frac{n v}{2L} $. First harmonic ($ n = 1 $): $ v_1 = \frac{340}{2 \times 0.85} = \frac{340}{1.7} = 200 \, \text{Hz} $.

Question 2

A string of length 1.8 m and mass 0.045 kg has a fundamental frequency of 40 Hz. What is the tension in the string?

Accepted Answer

$ \mu = \frac{0.045}{1.8} = 0.025 \, \text{kg/m} $. $ v_1 = \frac{v}{2L} \Rightarrow 40 = \frac{v}{2 \times 1.8} \Rightarrow v = 40 \times 3.6 = 144 \, \text{m/s} $. $ v = \sqrt{\frac{T}{\mu}} \Rightarrow 144 = \sqrt{\frac{T}{0.025}} \Rightarrow 144^2 = \frac{T}{0.025} $. $ T = 20736 \times 0.025 = 518.4 \, \text{N} $.

Question 3

A wave $ y = 0.04 \sin (30x - 60t) $ reflects at an open boundary. What is the equation of the reflected wave?

Accepted Answer

At open boundary, no phase change. Incident: $ y_i = 0.04 \sin (30x - 60t) $. Reflected: $ y_r = 0.04 \sin (30x + 60t) $.

NEET Physics: Waves — Practice Set 15

Q1. A pipe open at both ends has a length of 0.85 m and a speed of sound of 340 m/s. What is the frequency of its first harmonic?

Q2. A string of length 1.8 m and mass 0.045 kg has a fundamental frequency of 40 Hz. What is the tension in the string?

Q3. A wave \( y = 0.04 \sin (30x - 60t) \) reflects at an open boundary. What is the equation of the reflected wave?

Q4. A string fixed at both ends has a length of 2 m and a wave speed of 90 m/s. What is the frequency of its third harmonic?

Q5. A pipe closed at one end has a length of 0.5 m and resonates at its fundamental frequency with a speed of sound of 350 m/s. What is the frequency?

Q6. A stationary wave on a string fixed at both ends has a frequency of 100 Hz and a wave speed of 40 m/s. What is the length of the string?

Q7. A wave on a string has an amplitude of 0.02 m and a period of 0.01 s. What is the maximum transverse speed of a particle?

Q8. A transverse wave on a string has a speed of 30 m/s and a wavelength of 1.5 m. What is the time period of the wave?

Q9. A transverse wave on a string has a speed of 24 m/s and a period of 0.02 s. What is its wavelength?

Q10. Two waves of frequencies 465 Hz and 470 Hz interfere. How many beats are heard in 12 seconds?