NEET Waves — Set 2

Question 1

A pipe open at both ends has a length of 0.65 m and a speed of sound of 340 m/s. What is the frequency of its third harmonic?

Accepted Answer

For open pipe: $ v_n = \frac{n v}{2L} $. Third harmonic ($ n = 3 $): $ v_3 = \frac{3 \times 340}{2 \times 0.65} = \frac{1020}{1.3} \approx 784.62 \, \text{Hz} $.

Question 2

A longitudinal wave in a medium has a speed of 1500 m/s and a bulk modulus of 2.25 × 10⁹ Pa. What is the density of the medium?

Accepted Answer

Speed: $ v = \sqrt{\frac{B}{\rho}} $. $ 1500 = \sqrt{\frac{2.25 \times 10^9}{\rho}} \Rightarrow 1500^2 = \frac{2.25 \times 10^9}{\rho} $. $ \rho = \frac{2.25 \times 10^9}{1500^2} = \frac{2.25 \times 10^9}{2.25 \times 10^6} = 1000 \, \text{kg/m}^3 $.

Question 3

A copper rod of density 8960 kg/m³ has a speed of sound of 3600 m/s. What is its Young’s modulus?

Accepted Answer

Speed: $ v = \sqrt{\frac{Y}{\rho}} $. $ 3600 = \sqrt{\frac{Y}{8960}} \Rightarrow 3600^2 = \frac{Y}{8960} $. $ Y = 3600^2 \times 8960 = 1.16 \times 10^{11} \, \text{Pa} $.

NEET Physics: Waves — Practice Set 2

Q1. A pipe open at both ends has a length of 0.65 m and a speed of sound of 340 m/s. What is the frequency of its third harmonic?

Q2. A longitudinal wave in a medium has a speed of 1500 m/s and a bulk modulus of 2.25 × 10⁹ Pa. What is the density of the medium?

Q3. A copper rod of density 8960 kg/m³ has a speed of sound of 3600 m/s. What is its Young’s modulus?

Q4. What happens to the amplitude of two identical waves undergoing destructive interference when their phase difference is \( \pi \) radians?

Q5. A transverse wave on a string is described by \( y(x, t) = 0.04 \sin (60x - 15t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the speed of the wave?

Q6. What happens to the speed of a transverse wave on a string if the tension is doubled while keeping the linear mass density constant?

Q7. A pipe closed at one end has a length of 0.68 m and a speed of sound of 340 m/s. What is the frequency of its third harmonic?

Q8. A wave \( y = 0.07 \sin (25x - 50t) \) reflects at a rigid boundary. What is the equation of the reflected wave?

Q9. A transverse wave on a string has a tension of 150 N and a linear mass density of 0.02 kg/m. What is the frequency if the wavelength is 2.5 m?

Q10. A pipe closed at one end has a length of 0.36 m and a speed of sound of 324 m/s. What is the frequency of its third harmonic?

Q11. For a standing wave in a pipe open at both ends, which statement is true about the harmonic frequencies?

Q12. A string of length 2.1 m fixed at both ends has a wave speed of 63 m/s. What is the frequency of its fifth harmonic?

Q13. Which statement best describes the energy in a standing wave?

Q14. A string of mass 0.05 kg and length 5 m is under tension. If the speed of a transverse wave is 100 m/s, what is the tension?

Q15. Two waves of frequencies 520 Hz and 526 Hz interfere. How many beats are heard in 10 seconds?