NEET Waves — Set 17

Question 1

A string of length 2 m and mass 0.04 kg is under a tension of 100 N. What is the speed of a transverse wave on the string?

Accepted Answer

Linear mass density: $ \mu = \frac{0.04}{2} = 0.02 \, \text{kg/m} $. Speed: $ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{100}{0.02}} = \sqrt{5000} \approx 70.71 \, \text{m/s} $.

Question 2

A stationary wave is given by $ y = 0.06 \sin (\frac{\pi x}{2}) \cos (120\pi t) $, where $ x $ and $ y $ are in meters and $ t $ in seconds. What is its wavelength?

Accepted Answer

Form: $ y = A \sin (kx) \cos (\omega t) $, $ k = \frac{\pi}{2} \, \text{rad/m} $. $ \lambda = \frac{2\pi}{k} = \frac{2\pi}{\frac{\pi}{2}} = 4 \, \text{m} $.

Question 3

A pipe open at both ends has a length of 0.45 m and resonates with a source of frequency 1133 Hz. What is the harmonic number if the speed of sound is 340 m/s?

Accepted Answer

$ v_n = \frac{n v}{2L} $. $ 1133 = \frac{n \times 340}{2 \times 0.45} = \frac{n \times 340}{0.9} $. $ 1133 = n \times 377.78 \Rightarrow n \approx \frac{1133}{377.78} \approx 3 $. Third harmonic (exact: $ v_3 = 3 \times 340 / 0.9 = 1133.33 \, \text{Hz} $).

NEET Physics: Waves — Practice Set 17

Q1. A string of length 2 m and mass 0.04 kg is under a tension of 100 N. What is the speed of a transverse wave on the string?

Q2. A stationary wave is given by \( y = 0.06 \sin (\frac{\pi x}{2}) \cos (120\pi t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is its wavelength?

Q3. A pipe open at both ends has a length of 0.45 m and resonates with a source of frequency 1133 Hz. What is the harmonic number if the speed of sound is 340 m/s?

Q4. A stationary wave on a string fixed at both ends has a frequency of 120 Hz and a wave speed of 48 m/s. What is the length of the string?

Q5. A string of length 1.5 m fixed at both ends has a wave speed of 45 m/s. What is the frequency of its fifth harmonic?

Q6. Two waves of frequencies 500 Hz and 504 Hz interfere to produce beats. How many beats are heard in 10 seconds?

Q7. In a standing wave on a string, what is true about the energy at a node?

Q8. A pipe open at both ends has a length of 0.25 m and a speed of sound of 340 m/s. What is the frequency of its second harmonic?

Q9. Two waves \( y_1 = 4 \sin (6x - 18t) \) and \( y_2 = 4 \sin (6x - 18t + \frac{\pi}{3}) \) interfere. What is the amplitude of the resultant wave?

Q10. A longitudinal wave in a medium has a speed of 1450 m/s and a density of 1100 kg/m³. What is the bulk modulus of the medium?