📐 Chapter 12: Waves – Numerical Problems
Prepared by Muhammad Tayyab, Subject Specialist Physics, Govt Christian High School Daska. Based on PECTAA 2026 syllabus (National Curriculum 2023).
📖 What's Inside: This section covers numerical problems from the official PECTAA 2026 curriculum: wave speed calculation from wavelength & frequency, frequency from speed & wavelength, wavelength from frequency & speed, time period from frequency, and frequency from time period. Each problem includes step-by-step solutions using the wave equation \( v = f\lambda \).
📚 Related Resources – Chapter 12: Waves
Practice numerical problems to master wave equation calculations for board exams.
📖 Numerical Problems & Solutions (PECTAA 2026)
12.1 Wave Speed from Wavelength and Frequency
The wavelength of a wave is 2 metres and its frequency is 5 Hz. What is the speed of the wave?
📊 Given Data:
λ = 2 m, f = 5 Hz
λ = 2 m, f = 5 Hz
\[ v = f \lambda \]
\[ v = 5 \times 2 = 10 \text{ m/s} \]
✅ Answer: 10 m/s
12.2 Frequency from Wave Speed and Wavelength
A wave travels at a speed of 300 m/s and has a wavelength of 3 metres. Calculate its frequency.
📊 Given Data:
v = 300 m/s, λ = 3 m
v = 300 m/s, λ = 3 m
\[ v = f\lambda \implies f = \frac{v}{\lambda} \]
\[ f = \frac{300}{3} = 100 \text{ Hz} \]
✅ Answer: 100 Hz
12.3 Wavelength from Frequency and Speed
A sound wave has a frequency of 250 Hz and a speed of 340 m/s. Find its wavelength.
📊 Given Data:
f = 250 Hz, v = 340 m/s
f = 250 Hz, v = 340 m/s
\[ v = f\lambda \implies \lambda = \frac{v}{f} \]
\[ \lambda = \frac{340}{250} = 1.36 \text{ m} \]
✅ Answer: 1.36 m
12.4 Time Period from Frequency
A wave has a frequency of 50 Hz. How much time does it take to complete one wave?
📊 Given Data:
f = 50 Hz
f = 50 Hz
\[ T = \frac{1}{f} \]
\[ T = \frac{1}{50} = 0.02 \text{ s} \]
✅ Answer: 0.02 seconds
12.5 Wave Speed from Wavelength and Frequency
A wave has a wavelength of 0.5 m and frequency of 200 Hz. Calculate the speed of the wave.
📊 Given Data:
λ = 0.5 m, f = 200 Hz
λ = 0.5 m, f = 200 Hz
\[ v = f \lambda \]
\[ v = 200 \times 0.5 = 100 \text{ m/s} \]
✅ Answer: 100 m/s
12.6 Frequency from Time Period
The time period of a wave is 0.02 seconds. Calculate the frequency of the wave.
📊 Given Data:
T = 0.02 s
T = 0.02 s
\[ f = \frac{1}{T} \]
\[ f = \frac{1}{0.02} = 50 \text{ Hz} \]
✅ Answer: 50 Hz
📐 Key Formulas – Waves
Wave Equation: \( v = f \lambda \)
Time Period: \( T = \frac{1}{f} \) or \( f = \frac{1}{T} \)
Wave Speed: \( v = \frac{\lambda}{T} \)
💡 Exam Tip:
For numerical problems on waves, always remember the wave equation \( v = f\lambda \). Frequency is measured in Hertz (Hz), wavelength in metres (m), and speed in metres per second (m/s). Time period (T) is the time for one complete wave cycle. These problems follow the PECTAA 2026 pattern and are prepared by Subject Specialist Muhammad Tayyab.
Unit 10✨ Thermal Physics
Unit 11Transfer of Thermal Energy
Unit 12🌊 Waves (Current)
Unit 13Sound
Unit 14Light
Unit 15Electrostatics
Unit 16Electricity
Unit 17Electromagnetism
Unit 18Electromagnetic Induction & EM Waves
Unit 19Electronics
Unit 20Atomic and Nuclear Physics
Unit 21Space and Environment
📖 Complete syllabus coverage for Class 10 Physics (PECTAA 2026) – Units 10 to 21
Created by Hira Science Academy | Aligned with PECTAA 2026 Syllabus