Waves Solved Examples (Class 11 Physics)
Waves numericals cover wave equation, speed of sound, interference, and wave properties. These problems help understand sound propagation and optical pheno
TL;DR: Waves numericals cover wave equation, speed of sound, interference, and wave properties. These problems help understand sound propagation and optical…
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Waves numericals cover wave equation, speed of sound, interference, and wave properties. These problems help understand sound propagation and optical pheno
Waves — Solved Numerical Examples (Step by Step)
Example 1: A sound wave has frequency 500 Hz and wavelength 0.68 m. Calculate the speed of sound.
Solution: Frequency f = 500 Hz, Wavelength λ = 0.68 m. Speed v = f × λ = 500 × 0.68 = 340 m/s.
Example 2: A wave travels with speed 400 m/s and has a period of 0.01 s. Calculate wavelength and frequency.
Solution: Speed v = 400 m/s, Period T = 0.01 s. Frequency f = 1/T = 1/0.01 = 100 Hz. Wavelength λ = v/f = 400/100 = 4 m.
Example 3: A vibrating string of length 1 m vibrates in its fundamental mode. If the speed of waves on the string is 100 m/s, find frequency.
Solution: Length L = 1 m, fundamental mode (n=1). Wavelength λ = 2L = 2 m. Speed v = 100 m/s. Frequency f = v/λ = 100/2 = 50 Hz.
Example 4: Two coherent sound waves with frequencies 256 Hz and 260 Hz interfere. Calculate the beat frequency.
Solution: Frequency f₁ = 256 Hz, Frequency f₂ = 260 Hz. Beat frequency = |f₂ - f₁| = |260 - 256| = 4 Hz.
Example 5: A wave is described by y = 5 sin(2πx/4 - 2πt/0.01) cm. Find amplitude, wavelength, period, and wave speed.
Solution: From y = A sin(2πx/λ - 2πt/T), amplitude A = 5 cm. Wavelength λ = 4 cm. Period T = 0.01 s. Wave speed v = λ/T = 4/0.01 = 400 cm/s = 4 m/s.
Tips
- Wave speed v = frequency × wavelength (v = f × λ).
- Frequency and period are inverse: f = 1/T.
- Beat frequency is the absolute difference between two close frequencies.
Frequently Asked Questions
What is the difference between transverse and longitudinal waves?
Transverse waves vibrate perpendicular to the direction of propagation (e.g., light, water waves). Longitudinal waves vibrate parallel to propagation direction (e.g., sound).
Why do we hear beats when two nearby frequencies play together?
When two waves of slightly different frequencies interfere, they alternately add and subtract due to phase differences, creating a fluctuating sound intensity heard as beats.
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