NEET Waves — Set 21

Question 1

A pipe open at both ends has a length of 0.34 m and resonates with a source of frequency 1000 Hz. What is the harmonic number if the speed of sound is 340 m/s?

Accepted Answer

$ v_n = \frac{n v}{2L} $. $ 1000 = \frac{n \times 340}{2 \times 0.34} = \frac{n \times 340}{0.68} $. $ 1000 = n \times 500 \Rightarrow n = \frac{1000}{500} = 2 $. Second harmonic.

Question 2

Which property of a medium is most critical for the propagation of longitudinal waves through a gas?

Accepted Answer

Longitudinal waves in a gas rely on compressibility, quantified by the bulk modulus, which provides the restoring force for pressure oscillations, unlike shear modulus needed for transverse waves.

Question 3

A transverse wave on a string has a tension of 180 N and a linear mass density of 0.03 kg/m. What is the wavelength if the frequency is 20 Hz?

Accepted Answer

Speed: $ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{180}{0.03}} = \sqrt{6000} \approx 77.46 \, \text{m/s} $. Wavelength: $ \lambda = \frac{v}{v} = \frac{77.46}{20} \approx 3.87 \, \text{m} $.

NEET Physics: Waves — Practice Set 21

Q1. A pipe open at both ends has a length of 0.34 m and resonates with a source of frequency 1000 Hz. What is the harmonic number if the speed of sound is 340 m/s?

Q2. Which property of a medium is most critical for the propagation of longitudinal waves through a gas?

Q3. A transverse wave on a string has a tension of 180 N and a linear mass density of 0.03 kg/m. What is the wavelength if the frequency is 20 Hz?

Q4. A stationary wave on a string fixed at both ends has a frequency of 150 Hz and a wave speed of 45 m/s. What is the wavelength?

Q5. Two waves \( y_1 = 4 \sin (5x - 10t) \) and \( y_2 = 4 \sin (5x - 10t + \frac{\pi}{6}) \) interfere. What is the amplitude of the resultant wave?

Q6. A steel rod of length 1.5 m has a fundamental frequency of longitudinal vibrations of 2 kHz. What is the speed of sound in the rod?

Q7. Two waves of frequencies 510 Hz and 514 Hz interfere. How many beats are heard in 15 seconds?

Q8. A string of length 4 m and mass 0.08 kg is under a tension of 200 N. How long does a transverse pulse take to travel its length?

Q9. A string of length 3 m and mass 0.06 kg is under a tension of 150 N. What is the speed of a transverse wave on the string?

Q10. A pipe open at both ends has a length of 0.68 m and resonates with a source of frequency 750 Hz. What is the harmonic number if the speed of sound is 340 m/s?