NEET Waves — Set 20

Question 1

A stationary wave on a string fixed at both ends has a wavelength of 0.6 m and a frequency of 100 Hz. What is the wave speed?

Accepted Answer

Speed: $ v = v \lambda = 100 \times 0.6 = 60 \, \text{m/s} $.

Question 2

Two waves $ y_1 = 3 \sin (10x - 20t) $ and $ y_2 = 3 \sin (10x - 20t + \frac{\pi}{4}) $ interfere. What is the amplitude of the resultant wave?

Accepted Answer

Amplitude: $ A = 2a \cos \frac{\phi}{2} $, $ a = 3 \, \text{m} $, $ \phi = \frac{\pi}{4} $. $ A = 2 \times 3 \cos \frac{\pi}{8} \approx 6 \times 0.9239 \approx 5.54 \, \text{m} $.

Question 3

A pipe 0.5 m long, open at both ends, resonates with a 340 Hz source. What is the harmonic number if the speed of sound is 340 m/s?

Accepted Answer

For open pipe: $ v_n = \frac{n v}{2L} $. Given: $ v = 340 \, \text{m/s} $, $ L = 0.5 \, \text{m} $, $ v_n = 340 \, \text{Hz} $. $ 340 = \frac{n \times 340}{2 \times 0.5} \Rightarrow 340 = 340n \Rightarrow n = 1 $. First harmonic (fundamental mode).

NEET Physics: Waves — Practice Set 20

Q1. A stationary wave on a string fixed at both ends has a wavelength of 0.6 m and a frequency of 100 Hz. What is the wave speed?

Q2. Two waves \( y_1 = 3 \sin (10x - 20t) \) and \( y_2 = 3 \sin (10x - 20t + \frac{\pi}{4}) \) interfere. What is the amplitude of the resultant wave?

Q3. A pipe 0.5 m long, open at both ends, resonates with a 340 Hz source. What is the harmonic number if the speed of sound is 340 m/s?

Q4. A pipe closed at one end has a length of 0.85 m and resonates at its second harmonic with a speed of sound of 340 m/s. What is the frequency?

Q5. A string of length 2.5 m and mass 0.025 kg has a fundamental frequency of 40 Hz. What is the tension in the string?

Q6. A transverse wave on a string has a tension of 225 N and a linear mass density of 0.025 kg/m. What is the wavelength if the frequency is 30 Hz?

Q7. A pipe closed at one end has a length of 0.25 m. What is the frequency of its third harmonic if the speed of sound is 340 m/s?

Q8. A string of length 2.4 m fixed at both ends has a wave speed of 72 m/s. What is the frequency of its fifth harmonic?

Q9. Two strings produce beats of 8 Hz. One has a frequency of 440 Hz. When the tension in the second string is increased, the beat frequency becomes 6 Hz. What was the original frequency of the second string?

Q10. A stationary wave on a string is given by \( y = 0.08 \sin (2\pi x) \cos (100\pi t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the distance between two consecutive nodes?