NEET Waves — Set 22

Question 1

A string fixed at both ends has a length of 1.5 m and a fundamental frequency of 50 Hz. What is the speed of the wave on the string?

Accepted Answer

Fundamental frequency: $ v_1 = \frac{v}{2L} $. $ 50 = \frac{v}{2 \times 1.5} \Rightarrow 50 = \frac{v}{3} \Rightarrow v = 150 \, \text{m/s} $.

Question 2

A string of length 2 m and mass 0.01 kg is under a tension of 100 N. What is the time taken by a transverse pulse to travel from one end to the other?

Accepted Answer

Linear mass density: $ \mu = \frac{\text{mass}}{\text{length}} = \frac{0.01}{2} = 0.005 \, \text{kg/m} $. Speed: $ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{100}{0.005}} = \sqrt{20000} \approx 141.4 \, \text{m/s} $. Time: $ t = \frac{\text{length}}{v} = \frac{2}{141.4} \approx 0.014 \, \text{s} $.

Question 3

Two waves $ y_1 = 3 \sin (8x - 16t) $ and $ y_2 = 3 \sin (8x - 16t + \frac{2\pi}{3}) $ interfere. What is the amplitude of the resultant wave?

Accepted Answer

Amplitude: $ A = 2a \cos \frac{\phi}{2} $, $ a = 3 \, \text{m} $, $ \phi = \frac{2\pi}{3} $. $ A = 2 \times 3 \cos \frac{\pi}{3} = 6 \times \frac{1}{2} = 3 \, \text{m} $.

NEET Physics: Waves — Practice Set 22

Q1. A string fixed at both ends has a length of 1.5 m and a fundamental frequency of 50 Hz. What is the speed of the wave on the string?

Q2. A string of length 2 m and mass 0.01 kg is under a tension of 100 N. What is the time taken by a transverse pulse to travel from one end to the other?

Q3. Two waves \( y_1 = 3 \sin (8x - 16t) \) and \( y_2 = 3 \sin (8x - 16t + \frac{2\pi}{3}) \) interfere. What is the amplitude of the resultant wave?

Q4. Why are standing waves formed in musical instruments like a guitar?

Q5. A steel rod of length 2 m has a fundamental frequency of longitudinal vibrations of 1.25 kHz. What is the speed of sound in the rod?

Q6. Two strings produce beats of 4 Hz. One has a frequency of 320 Hz. When the tension in the second string is increased, the beat frequency becomes 2 Hz. What was the original frequency of the second string?

Q7. A string fixed at both ends has a length of 1.6 m and a fundamental frequency of 62.5 Hz. What is the speed of the wave?

Q8. A string of length 2.2 m fixed at both ends has a wave speed of 66 m/s. What is the frequency of its fourth harmonic?

Q9. A string fixed at both ends has a length of 1.4 m and a wave speed of 70 m/s. What is the frequency of its second harmonic?

Q10. Which wave property is most affected when a sound wave encounters a change in the medium’s temperature?