NEET Waves — Set 19

Question 1

Two waves of frequencies 480 Hz and 486 Hz interfere. How many beats are heard in 12 seconds?

Accepted Answer

Beat frequency: $ v_{\text{beat}} = 486 - 480 = 6 \, \text{Hz} $. Beats in 12 s: $ 6 \times 12 = 72 $.

Question 2

A stationary wave is given by $ y = 0.05 \sin (\frac{\pi x}{2}) \cos (100\pi t) $, where $ x $ and $ y $ are in meters and $ t $ in seconds. What is the distance between a node and the next antinode?

Accepted Answer

Form: $ y = A \sin (kx) \cos (\omega t) $, $ k = \frac{\pi}{2} \, \text{rad/m} $. Wavelength: $ \lambda = \frac{2\pi}{k} = \frac{2\pi}{\frac{\pi}{2}} = 4 \, \text{m} $. Distance between node and antinode: $ \frac{\lambda}{4} = \frac{4}{4} = 1 \, \text{m} $.

Question 3

A pipe closed at one end has a length of 0.4 m and a speed of sound of 320 m/s. What is the frequency of its fundamental mode?

Accepted Answer

Fundamental: $ v_1 = \frac{v}{4L} $. $ v_1 = \frac{320}{4 \times 0.4} = \frac{320}{1.6} = 200 \, \text{Hz} $.

NEET Physics: Waves — Practice Set 19

Q1. Two waves of frequencies 480 Hz and 486 Hz interfere. How many beats are heard in 12 seconds?

Q2. A stationary wave is given by \( y = 0.05 \sin (\frac{\pi x}{2}) \cos (100\pi t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the distance between a node and the next antinode?

Q3. A pipe closed at one end has a length of 0.4 m and a speed of sound of 320 m/s. What is the frequency of its fundamental mode?

Q4. When two waves interfere constructively, what happens to the resultant intensity if their amplitudes are equal?

Q5. The speed of sound in air at STP is calculated using Newton’s formula as 280 m/s. If the actual speed is 331 m/s, what is the value of \( \gamma \) (ratio of specific heats) for air?

Q6. A pipe closed at one end has a length of 0.6 m and resonates at its second harmonic with a speed of sound of 360 m/s. What is the frequency?

Q7. A string fixed at both ends has a length of 1.8 m and a wave speed of 54 m/s. What is the frequency of its third harmonic?

Q8. A stationary wave on a string fixed at both ends has a frequency of 90 Hz and a wave speed of 36 m/s. What is the length of the string?

Q9. Two waves of frequencies 475 Hz and 480 Hz interfere. How many beats are heard in 20 seconds?

Q10. A transverse wave on a string has a speed of 18 m/s and a frequency of 6 Hz. What is its wavelength?