NEET Waves — Set 16

Question 1

A string of length 1.2 m fixed at both ends has a wave speed of 48 m/s. What is the frequency difference between its fourth and second harmonics?

Accepted Answer

$ v_n = \frac{n v}{2L} $. Second harmonic ($ n = 2 $): $ v_2 = \frac{2 \times 48}{2 \times 1.2} = \frac{96}{2.4} = 40 \, \text{Hz} $. Fourth harmonic ($ n = 4 $): $ v_4 = \frac{4 \times 48}{2 \times 1.2} = \frac{192}{2.4} = 80 \, \text{Hz} $. Difference: $ v_4 - v_2 = 80 - 40 = 40 \, \text{Hz} $.

Question 2

What happens to the wavelength of a wave when it reflects off a free end without changing the medium?

Accepted Answer

Reflection at a free end does not alter the medium’s properties (tension, density), so the wave speed and frequency remain unchanged, keeping the wavelength constant ($ \lambda = v/f $).

Question 3

Two waves $ y_1 = 6 \sin (8x - 16t) $ and $ y_2 = 6 \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 = 6 \, \text{m} $, $ \phi = \frac{2\pi}{3} $. $ A = 2 \times 6 \cos \frac{\pi}{3} = 12 \times \frac{1}{2} = 6 \, \text{m} $.

NEET Physics: Waves — Practice Set 16

Q1. A string of length 1.2 m fixed at both ends has a wave speed of 48 m/s. What is the frequency difference between its fourth and second harmonics?

Q2. What happens to the wavelength of a wave when it reflects off a free end without changing the medium?

Q3. Two waves \( y_1 = 6 \sin (8x - 16t) \) and \( y_2 = 6 \sin (8x - 16t + \frac{2\pi}{3}) \) interfere. What is the amplitude of the resultant wave?

Q4. A string of length 0.9 m fixed at both ends has a wave speed of 45 m/s. What is the frequency difference between its second and first harmonics?

Q5. A transverse wave travels on a string with a tension of 200 N and linear mass density of 0.025 kg/m. What is the wavelength if the frequency is 40 Hz?

Q6. Two strings produce beats of 7 Hz. One has a frequency of 392 Hz. When the tension in the second string is increased, the beat frequency becomes 5 Hz. What was the original frequency of the second string?

Q7. Two waves \( y_1 = 4 \sin (5x - 15t) \) and \( y_2 = 4 \sin (5x - 15t + \pi) \) interfere. What is the amplitude of the resultant wave?

Q8. A pipe closed at one end has a length of 0.35 m and resonates at its fundamental frequency with a speed of sound of 350 m/s. What is the frequency?

Q9. Why does the speed of sound increase with temperature in a gas?

Q10. Which wave phenomenon is responsible for the cancellation of sound in certain regions when two speakers emit waves of equal frequency?