NEET Waves — Set 11

Question 1

A pipe closed at one end has a length of 0.8 m and resonates at its third harmonic with a speed of sound of 360 m/s. What is the frequency?

Accepted Answer

For closed pipe: $ v_n = (n + \frac{1}{2}) \frac{v}{2L} $, $ n = 2 $ for third harmonic. $ v_2 = (2 + \frac{1}{2}) \frac{360}{2 \times 0.8} = 2.5 \times \frac{360}{1.6} = 2.5 \times 225 = 562.5 \, \text{Hz} $.

Question 2

A pipe closed at one end has a length of 0.45 m and a speed of sound of 360 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{360}{2 \times 0.45} = 4.5 \times \frac{360}{0.9} = 4.5 \times 400 = 1800 \, \text{Hz} $.

Question 3

A string of length 2.8 m and mass 0.07 kg has a fundamental frequency of 35 Hz. What is the tension in the string?

Accepted Answer

$ \mu = \frac{0.07}{2.8} = 0.025 \, \text{kg/m} $. $ v_1 = \frac{v}{2L} \Rightarrow 35 = \frac{v}{2 \times 2.8} \Rightarrow v = 35 \times 5.6 = 196 \, \text{m/s} $. $ v = \sqrt{\frac{T}{\mu}} \Rightarrow 196 = \sqrt{\frac{T}{0.025}} \Rightarrow 196^2 = \frac{T}{0.025} $. $ T = 38416 \times 0.025 = 960.4 \, \text{N} $.

NEET Physics: Waves — Practice Set 11

Q1. A pipe closed at one end has a length of 0.8 m and resonates at its third harmonic with a speed of sound of 360 m/s. What is the frequency?

Q2. A pipe closed at one end has a length of 0.45 m and a speed of sound of 360 m/s. What is the frequency of its fifth harmonic?

Q3. A string of length 2.8 m and mass 0.07 kg has a fundamental frequency of 35 Hz. What is the tension in the string?

Q4. A pipe open at both ends has a length of 0.425 m and resonates with a source of frequency 800 Hz. What is the harmonic number if the speed of sound is 340 m/s?

Q5. Two strings produce beats of 5 Hz. One has a frequency of 256 Hz. When the tension in the second string is decreased, the beat frequency becomes 3 Hz. What was the original frequency of the second string?

Q6. Which property of a sound wave is most directly responsible for its loudness?

Q7. Which type of wave cannot propagate through a vacuum?

Q8. A pipe open at both ends resonates at 510 Hz with a speed of sound of 340 m/s. What is its length?

Q9. Two sitar strings produce beats of 5 Hz. If one has a frequency of 320 Hz and tension in the other is reduced, the beat frequency increases to 7 Hz. What is the original frequency of the second string?

Q10. A longitudinal wave in a medium has a speed of 1600 m/s and a bulk modulus of 2.56 × 10⁹ Pa. What is the density of the medium?